"More advanced" cameras are gonna cost more than your budget. I'm just saying that a more expensive or "advanced" camera body isn't going to get you noticeably different results for a few years. You're generally paying for features like higher resolution rear screen, tilt screen, maybe touch screen, maybe wifi that has poor reviews, etc. until you get to something like the 80D - and even then your sensor will only be marginally better.
Here's that T5 package for - omg $350!? You could get this AND a brand new 50 1.8 STM and meet your budget. These are the three lenses I'm still shooting and they're great. Hell, you could ask for a beefy speedlight for a birthday gift and you'd be outfitted for a semi-pro level work already.
If you have the cash for it, sure get more fun features, but $500 won't necessarily get you much more quality or useful features per dollar - even used. I just mentioned the T5 as a baseline because it's pretty bare bones as far as bells and whistles go and I'm still really impressed with it. The resulting image quality will still be 95-99% as good as much more expensive cameras. My point was just that even if you were to go super "intro" you'll have a great piece of equipment that will last. Even after 5+ years, I'm buying better glass and I'm not really limited by the camera body. If I were to upgrade the camera, I'd definitely continue taking the old T5 on bigger shoots to avoid having to change lenses in the field and I'd be happy to go back to it.
https://www.amazon.com/YONGNUO-YN600EX-RT-II-Wireless-Speedlite/dp/B01N21BEMD/ for the flash
https://www.amazon.com/YN-E3-RT-E3-RT-Speedlite-Wireless-Transmitter/dp/B00J2MR974 for wireless trigger unit (will need a trigger unit that supports TTL)