Is it possible to increase my site's SEO by getting blogs/other websites to provide back links to my site?

Stoney is on the money here.

The answer is really yes and no. Yes you want to get links, but no you don't want crappy links in high volume all pointing to the same page with the same optimized anchor text.

I totally agree to Stoney deGeyter. 5000 backlinks sounds like spam. It's almost impossible to get so many good ones, except your Tim Cook ;-). Better focus on good contents and some high quality backlinks with real traffic. And don't buy any backlinks!

I think Stoney is on the right track here, but the only thing that's missing is that this question cannot be answered correctly without actually knowing the industry and current leaders. There are different industries and topics that Google has different tolerances for. If authority websites on your topic commonly have/receive lots of backlinks from bloggers, you have more room to play with in this area. Also, social media is not a requirement for SEO. We've seen plenty of sites outranking competitors with no social presence at all. There is no one formula for what SEO should look like across all industries. The only place I'd say you're definitely looking at raising a red flag is with the anchor text. In your example you said you'd want thousands of links back using the same keyword. Chances are, no matter what your topic or industry, that's going to look very out of the ordinary. A natural looking, balanced link portfolio is really key these days in offsite optimization. You'll get all sorts of people these days that tell you to "build content people love" and SEO just happens. That's not the case, especially in an industry with any competition at all. SEO is a deliberate, calculated marketing strategy. If you feel that you're in an industry that's even remotely competitive, then I'd recommend seeking out an SEO agency with a solid reputation. If you're bootstrapping a business and looking to do whatever you can on your own, then I'd start by educating yourself on SEO from reliable resources such as: https://moz.com/learn/seo. (I'm not affiliated with Moz in any way). Best of luck!

Why try to get "toys"? Why not a long-tail keyword? It's going to be impossible to get "toys". (Unless you are rewarded by Google for being local) You'll be competing with informational results like Wikipedia and queries like "what are toys".
Be specific. "Toys for children under five" or specific toys, balls, rattles. Long tails will have more of a buyer intent.
5000 links to toys, that's just silly.

Probably Not Mine answer because of some issue
Recently updates from google Anchor text most import topic on the eyes of google engineers,Anchor text Distribution is more important in Link Building May be your Site Ranked Some Time But Its not working Proper Because its lose your Visitors in Future

In addition to these good answers you are receiving from these other experts, I would like to add another consideration, and that is you would be wise to be careful in your selection of bloggers to approach. It is not about quantity but quality. You should research who are the bloggers who are key influencers in the subject(s) most related to your product or service. Then review their sites, policies, and media kits if they have one. Some bloggers accept guest posts, many do not, almost all will charge a fee for product reviews and sponsored posts. Do not contact any one blogger until you determine that he or she seems to be a good fit for your purposes. Then you will see if that blogger is interested in working with you. The generic approach is a poor strategy - bloggers are individuals and no two are exactly alike.

I believe the answer to your question is simply no, as it is not possible to increase your SEO only by getting blogs/other websites to provide back links to your site. If you want to really increase your SEO here are the following tips that will help you:
1. Useful, high quality, relevant content: “Dwell time” is the amount of time visitors spend on your website and it can affect SEO ranking. When you provide useful content, visitors tend to stay longer on your website to consume the information and therefore increase the dwell time. Based on this research, content between 2,000 – 2,500 words seems to rank the highest in search engine results. Although word count doesn’t rule the SEO world – nobody will read your stuff if it’s not helpful to them – longer content does give you the opportunity to provide more value, include more keywords, incorporate more outbound links, and of course, get people to spend more time reading to increase dwell time. Another reason to create incredibly useful content is that when visitors bookmark your content on Chrome, it will improve SEO ranking of your website in Google.
2. Page load speed: Both Google and Bing take page-loading speed into account in their website ranking algorithm. Users may leave your site if they must wait even just an extra few second for each page to load. That would hurt your dwell time, increase your bounce rate, and reduce the number of pages viewed – all of which could hurt your SEO ranking. There are many ways to increase page load speed, some of which include using a caching plug-in, making sure the code is clean and streamlined, optimizing image sizes, reducing the number of plug-ins, and minimizing redirects. Research has shown that using good quality images can increase conversion rate. Properly optimizing your images can help you take advantage of using photos to generate empathy, increase trust, and improve a visitor’s experience without hampering load time which could affect your SEO ranking.
3. Image optimization: Besides image file format and sizing, there are other ways to make sure your images are working hard for you on the SEO front. You can signal relevancy of your content to search engines by using keywords for your image file name, alt tag, title, description, and caption.
4. Header tags: Nobody likes running into a wall of text. Good formatting of your content helps improve the user experience of your website tremendously. It makes readers more willing to spend time to read your content and come back for more, which will ultimately signal your relevancy to search engines. Proper use of header tags can help break up your content into sections that are easier to read and utilize. It is easy to insert header tags in WordPress to improve user experience and improve SEO ranking of your website. Search engines also rate keywords in header tags more heavily. By including relevant terms in your header tags, you are also boosting your SEO ranking against those keywords.
5. Outbound links: To make your content more useful and relevant, you can link out to authority sites for more in-depth information your readers can use. Linking out to well-respected authority sites will not only increase the relevancy of your content and time readers spend on your site, but it is also believed to send trust signals to Google and improve SEO ranking. However, more is not necessarily better. Too many outbound links can be distracting and make the content hard to get through.
6. Different multimedia: Images, videos, slideshows, and audio can help enrich the user experience and allow you to deliver information in a way that is most suited to your ideal site visitors. They also act as a signal of quality content to search engines after all, you have put in the work to make your content look good and interactive.
Video marketing has become an increasingly integral element in driving user engagement and conversion. It is found that websites using videos can achieve a 4.8% higher conversion rate, compared to a 2.9% average on websites that do not use videos.
7. Broken links: Who wants to get a 404 page after clicking on a link? Broken links make for bad usability. Not only that, search engines consider many broken links as a signal of an old, neglected site and this can impact your SEO ranking.Thankfully, you do not have to go through every single page on your website and test the links manually. There are many tools and apps to help ensure that your site is free of broken links, such as:
1. Screaming Frog SEO Spider
2. Google Webmaster Tool
3. W3C Link Checker
8. Readability: Even if you have a well-educated audience, they probably don’t want to be deciphering a PhD dissertation every time they visit your website and read your content. You do not want them to give up reading your content and click away because it is too difficult to digest. Making your content easy to read and understand helps make it useful to your readers. Some experts also believe that Google takes readability into account when ranking webpages. You can use a variety of tools to test your content’s readability, including:
1. Readability-Score.com
2. The Readability Test Tool
3. Readability statistics in MS Word

9. Layout and formatting: Proper formatting and a user-friendly layout can help improve user experience and make your content easy to scan and digest, so your readers will stay on your site longer and consume your website’s information. Formatting can help dramatically improve a webpage’s usability by making the content easy to read:
1. Use font size and typography that are easy to read.
2. Use bold type and colours – sparingly and strategically – to call out important information and make the content easy to scan.
3. Use short paragraphs and ample line spacing in between – nobody likes a wall of text.
4. Use bulleted or numbered lists for clarity.
5. Use techniques such as sliders, tabs, progressive layouts, structured grids, modal windows, rollover elements, accordions, and mega drop-down-menus to organize content and add interactivity.
6. Break up content into sections with subheads. Proper use of header tags that include keywords also helps improve SEO ranking.

10. Contact us page: According to this Google document (p.98), websites that have sufficient contact information are more trust-worthy and therefore may rank higher by search engines. Including a Contact Us page on your website and putting the link in the navigation not only makes for good user experience (especially if you have an ecommerce site) but can also potentially earn you some Google juice. It is found that a well-designed contact form increases user participation in a company’s online presence. It also helps generate new business opportunities, capture new leads, improve customer service, and more.
11. Site architecture and navigation: When visitors cannot find what they need on a website right away, they most likely leave the site and this contributes to high bounce rate, low dwell time and low number of pages viewed. A well-thought-out site architecture reflected in clear navigation is critical in helping visitors find what they want on your site, accomplish their goals, and come back repeatedly (repeated visits can improve SEO ranking.) A “flat” site architecture not only makes content easier to find, it can also help improve SEO ranking as it surfaces links of all critical pages making it easier for search engines to crawl the entire site.
12. Mobile optimization: As of April 2015, Google has started to penalize sites that are not mobile optimized by bumping down their search engine ranking. More and more users are consuming content on mobile devices, and not being mobile optimized is going to affect user experience and conversion. It is particularly important for B2B marketers. Research has shown that 77 percent of executives use their smartphone to research a product or service for their business. Business executives use mobile devices to research products and services for their businesses. It is not just for B2B websites either. Companies like Yelp that act as search directories connecting consumers to businesses found that 55% of all searches comes from mobile devices. If your website has been around for a while, it is time to test it to make sure it is compliant.
13. Social sharing: The number of Facebook shares, Tweets, Pinterest pins and other social media mentions can influence SEO rank. Installing social sharing buttons on your website not only makes it easy for users to share your content, and thereby improve user experience, it can also help you rank higher on searches. Social sharing also helps drive purchasing behaviour: Nearly 4 in 10 Facebook users report they have gone from liking, sharing or commenting on an item to actually buying it, while 43% of social media users have purchased a product after sharing or liking it on Pinterest, Facebook or Twitter. In this case study, a pest control company boosted organic traffic by 15% in just 2 weeks after running a campaign aimed to increase social sharing. Peep Laja managed to get over 40,000 unique visits to his site in month number one, having most of the traffic generated through social media sharing.
To get you started, here are a few social share button plug-ins to try:
1. SumoMe
2. Shareaholic
3. WP Social Sharing
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath