If you don't have a gym membership, just start doing the things you can do at home with a pullup bar, bands, and dumbbells.

Pushups, curls, db overhead press, db rows, db bench. Just look around on the internet/youtube and you can find a load of stuff to do.

I'd personally do an upper body routine 2-3x per week.

I know you said you can only do about 5 pushups now. Start with a couple sets of 5. next week go for a couple sets of 6 and so on. The key to getting stronger is to progressively increase the amount of work you're doing.