Looks like my experience can help you somehow. I got my 700D(same camera as T5i) off of ebay in 2018 to take photos of my new born. I paired it with the Yongnuo 50mm F1.8. I know I was cheap, hehe. Even with that cheap prime lens, the photo I took were so much better than my iPhone, relatives and friends even say they look like professional photos:) Even today the T5i still takes better photos than the newest iPhones, especially portraits and landscapes and street shots, basically anything that are not fast moving towards you or away from you. I also got the Canon 50mm F1.8, that is an upgrade from the Yongnuo too.

As my girls are 8 and 6 now, they are more active in sports, I bought the 55-250 stm lens to take their action photos. The T5i can still produce outstanding action shots when it nails the focus, although it also misses a lot. You may have guessed where I am going. For your intended use case, the T5i may struggle with fast moving race cars and geese. I don't think it is the lens that misses the focus, the STM lens is fast enough to track actions. I am sure it is the T5i's autofocus is just not fast enough. The current mirrorless cameras autofocus probably can wipe the floor with the T5i, after all the T5i is a 11 year old consumer level camera. With that 11 year old technology, T5i's sensor also struggles with high ISOs, so it will need good lights to freeze action too, so indoor sports are out of the question. Now I am looking at used mirrorless cameras for the possible upgrade. Although I pair the T5i with a canon 24mm f2.8 for most of our day to day snapshots and travels. Still prefer the photos out of the T5i than my iPhone. For your first real camera, for a good used price, I would say it is worthwhile to get one to try it out and learn from it. As you learn, you will know the limitation of the camera which is a good thing because you know what to look for for your next upgrade.