Since you shoot motorsports, and sometimes a portrait, I don't think you're going to really get everything you think you're going to get from fullframe by going to the 5D classic. The internet will have you believe that fullframe is magic. But today's modern APS-C is better than the 5D was. So really, I would say that if you want the least expensive full frame for the purpose of the thinnest tightest depth of field control, the 5D can be that for you. If you want to continue shooting sports, and you want a much better sensor, dynamic range, etc, but are on a budget, then look to a modern APS-C, like a used T5i, 60D, even a 7D is becoming affordable.
I shoot a 5D classic myself, as my full frame, but only for portrait. I use modern APS-C for everything else (landscape, wildlife, macro, astro, you name it). I don't recommend the 5D as a cure all, because it's not the most robust camera these days for sports, it's ISO is quite limited by today's standards, it's resolution limits cropping, it doesn't have fast FPS (not that it's a big deal though really), etc.
I like my 5D. Great for using a viewfinder. Great for manual glass. But no Live View. It's autofocus is not something I'm impressed with by any means. It's ISO performance is ok, but it's not what you can get on even a modern APS-C. I look at the 5D as one of those good cameras for general photography and especially for portraiture for today. And that's what I use it for.
Otherwise, again, I would recommend a T5i, 60D, or 7D instead for what you're describing, on a budget, as a hobbyist. Full frame doesn't just change the game for you. It's just another tool, and if you don't have a need for what it offers, then it's not really the right tool every time. Also consider, 300mm on full frame, is not what you're used to seeing on APS-C. Huge difference in field of view. So you'll be cropping to get the same frame up you're used to from the same distance.