Everyone who picks up a racket for the first time is admittedly bad at it, so all professional players went from less than 2.5 to a full 7.0.
However, if you want to play 5.0 or even above, down from a 2.5 level, you'll need to work hard and for a long time. Professional players atop of their game usually are in their mid 20s and have spent well over a decade perfecting their game, spending thousands of hours on the court and at the gym, so you're up for some serious work if you intend on reaching that high a level of play.
I also want to make you realize something. At a certain point in a player's development, tennis stops being a hobby. I'd tempted to say that for many 5.0 or higher players, tennis is a life style. We're talking about people hitting a few times per week, getting private lessons ocassionally, attending tournaments or partaking to league matches. Those people don't work as tennis players, so they have a job and hence all of those things must take place in whatever spare time is left after their weekly chores and working hours. So a lot of their spare time is dedicated to playing tennis, improving their game or training to get in better shape.
If your goals in life include a certain career path, perhaps also owning your own place and starting a family, or maybe travelling a bit, it will be very difficult to get to a 5.0 level of play, let alone going beyond that because time will be too scarce. People comment here about athleticism, but your primary problem will be time and unless some of your goals besides tennis include aspects that are tennis-related, you'll have to make choices about what you prefer to keep and what you will give up.
I also wanted to finish this post on a more enjoyable note, something more encouraging that will keep you happy working on your game. It might not seem like that when you're on the sidelines or when you look at videos, but even 4.5 players play extremely well. When you put yourself in front of those shots, you can realize it's not easy at all to keep up, no matter what you try to do with them. I know that people on this forum will be excessively picky on technical details and will routinely underrate otherwise very good players just because this or that stroke doesn't look as neat as it should, but as they say the proof is in the pudding: when you get them to play against other 4.5 players you realize that those idyosincracies and special habits of theirs work very well at that level.
Moreover, there is something else to tennis than your playing level. It is supposed to be a fun game, something you enjoy doing. Of course, just like everybody on this forum, I love to see myself doing things I thought I couldn't do, or learning to do things I knew I couldn't do before. This sort of surprise, of knowing you're moving forward in some sense, is very satisfying. It is also nice to win matches every now and then. In other words, results can be part of the fun. They just aren't the whole of the fun. Yesterday, I played a set and tried a few things like hitting slice serves and serving and volleying on all service points. I lost, but the feeling of moving forward, trying to make sure my transition volley does something and playing more with touch shots than usual was very satisfying. For me, tennis is also about the "I got you" moments, where you go out and you outsmart your opponent -- and it was also nice to see my opponent respond. My personal goal for tennis is to get my game to a point where intentions matter more often so that I get to live more of those moments on the court.
