But right now I'm still learning so I can't build anything major yet beyond random number generators and guessing word games. But I'll get there.
Next I'll learn JQuery and Ajax.
Is it possible to work in programming as a student while learning how to program?
Even making $5/hr would be amazing because I would be using what I'm learning and building a portfolio.
Most jobs in the marketplace are going to require more skill and experience than you have currently. One avenue that may allow you to make some money while expanding your skills would be to bid on projects through the platform upwork.com. This is a platform designed to help people find freelancers to assist with various projects.
Upwork.com has a constant stream of web development project of all shapes and sizes. You may be able to find some projects there that fit within your skillset and bid to complete them.
Another unpaid opportunity could be to begin writing free/open source scripts, utilities, or tools and post them for public use. This would allow you to expand your capabilities while also building a body of work that you could show potential clients or employers as your skills improve and you begin seeking employment. Look for common problems and find ways to solve them. Even if there are other solutions out there you can exploit your limited knowledge to create simple straight-forward solutions for other beginners like yourself who can often be overwhelmed by some of the more complex solutions and frameworks common in the marketplace.