Assalamu alaykum,
There's no reason why because of salah you can't play basketball.
Usually the time frames between salah aren't any less than two hours - for example here in the UK at the moment, Dhuhr is at 12:20 and Asr is at 3pm, more than enough time to do whatever you want.
And besides, especially as a brother you don't have to pray salah at home. If there's a mosque nearby where you play you can go there for prayer, or if not you can always pray in a park or quiet place with some other brothers and then just get back to your game - it would take less than 15 minutes and you can play basketball for as long as you want, as long are you read your salah on time inshaAllah..