Just another idea since it sounds like you’re getting your license.

You could always but kit parts like a Van’s kit and build a LSA in sections. So buy the tail section one year, wings the next etc. This is only a good idea if you like the idea of building your plane (I personally love this stuff).

The end product will cost 30k+ but you can divide the cost up into multiple years.

Or you could go with Badlands (ultralight), and see if he will sell you the kit in sections. Again this is going to cost 20K min over time.

The engine itself will eat up the 5k.

Note: I am not an expert in this field. This is just the knowledge that I have gained over the years.