Do angel investors look for a certain number of active users when investing in an app startup that has recently launched, 5,000-10,000+?

First of all, there is no "one size fits all" attitude in angel investing. I will tell you that the *best* angels will make a snap decision by playing with the product and assessing founder/market fit. At the right valuation, the kinds of angels you really want backing you will invest purely based on a killer early product experience and conviction of founder/market fit.

But if you have made your app available in the US app store already, you have made a critical tactical error if your app isn't already trending towards 100,000 installs within the first 30 days of availability. Apps should first launch in a non US, english-speaking store to do early product/market fit work.

Your "day one" event in the US app store matters to seed investors and many angel investors. While there are exceptions (most often in SaaS or enterprise mobile models), there are only 4 times to raise funding from seed funds for a mobile start-up stage company:

Pre-product: A deck, a market opportunity and a team.
Pre-launch: Product fully built but holding launch for funding. This will usually involve a private beta of at least 1000 users or a soft launch in an international store.
30 - 90 days after US launch: Must be at or trending towards 100,000 installs with very strong month-over-month growth.

If you miss those windows, the next time to raise is after you pass over 1,000,000 with strong retention and engagement that correlates to your business model and user personas.

As a mobile-first entrepreneur and angel investor, I'm happy to talk to you about this in more detail

they look for traction, meaning they look for a tendency of growth and behaviour that will allow them to predict what could the outcome be if "fueled" by additional capital.

A stat is just a stat, it needs to show how it is behaving or compares to other similar apps.

Not necessarily, but certainly, the more the better. Ultimately, we're looking for 1) proof that the market cares about your offering, and 2) management traction.

Essentially, we're looking for ways to remove risk from the investing equation, so anything you can do to remove risk from the equation makes your investment more attractive. This translates into increased investor interest and greater valuations for you.

Put your investor cap on and find all of the things you might be worried about as an investor (adoption/attrition rates, customer acquisition costs, etc.) and have/create good answers for how you can mitigate or have mitigated those risks, or why the trend is positive. Back it up with numbers wherever possible.

Forget specific numbers, and make sure the underlying business trends are positive.

The trend is your friend. Good luck!

Users are a sign of traction a.k.a. proof of concept. Most angel investors want to fuel growth and help you strive for product market fit. If you're following the lean startup model - most angels will only engage once you found problem solution fit and are reaching for product market fit.

That being said 10,000 users is a typical benchmark.