Well, not much athletic genes, much more on the intelligence/academic side which still helps I'd say.
Tennis is my main sport. Before tennis, I kept in shape by running (excessively) and weight lifting.
I don't think the key is private lessons for me anymore. I've had enough to know all the proper strokes (or so I think). I just need to rally and play with other people. After doing that for a bit, I guess I can go back to a different coach for a second opinion on proper strokes, footwork, etc.
I just like to think I can still do it, even with all the distractions I'm facing (I am a fulltime student).
My background: play American sports as a child: baseball, football, and made all-star baseball teams. Took up tennis at around age 20 - am now 54 years old. Played on 4.5 city championship team and won all matchs in city playoffs - 3 playoff level rounds. Played a few seasons at 5.0 and won about 50% of time. Now play in 4.5 singles leauge on web and play in non-usta doubles leauge around the same level.
My suggestions:
1. If you can afford it, try to keep up the lessons. As others said above, a good foundation is critical. Semi-private lessons with a friend - maybe 4-6 lessons in the spring, and occasional adult camps would be great. I attended a couple of adult camps when younger with 3 hour a day format for a week and these really help. Lifts your game for a few months.
2. Read books and watch videos. Some may say stick only with what your coach says, but I think you can learn a lot from reading and watching video. Realize some methods you read may even have contradicting views and you have to learn to sift through the different views.
3. Play at the appropriate level. Playing good players helps. So, once you start winning 75% of your matches, you may want to try playing up to the next level. When you are winning about 50% of your matches, you are playing at the right level. Try to practice with higher ranked players if possible.
4. Play and practice at least 4 times a week for next few years until you get to your highest level. Also, continue to work on fitness - movement is critical to good tennis. I know as it is harder and harder to move well with each passing year at my age.
5. Join internet singles leauges, tournaments and doubles leauges, and teams in your area. Team play and leauge play is the best way to meet friends to practice with and it exposes you to a variety of different players.
But, even if you do not make 5.0 level, still enjoy the game. Tennis is a great game, and 2 evenly matched players at any level can have an entertaining and fun match. I have watched 3.5 level matches that were really fun when the matches are close. Also, 4.0 and 4.5 are pretty damn tough levels. If you can get to this level, you are proably ahead of 80% of the tennis playing population. I have played teaching pros and instructors at 4.0 and 4.5. One of the 4.5 players was an older pro who had played the satiellite circuit when he was younger - he was in his late 50s/early 60s now. So, you will play good players at these levels.
I SWAG for how long to become 5.0 - my experience would be at least 5-10 years. If gifted, maybe less.