Will exercising 5 minutes a day help build my muscles?

Absolutely not. You have to exercise literally. All. Day. Long.

If 5 minutes a day of exercise is tough, do that. But if you aren’t even getting your heart rate up, your muscles aren’t at all excited and you haven’t broken a sweat, I ask you: what are you willing to do to build your muscles? It’s in the nature of the word:

Build. That means to overload the muscles so that they tear, and then recover as stronger muscles. If you can do that on 5 minutes a day, kudos.

5 minutes a day is too little. You’ll need around 10-15 minutes for a warm up and stretching before you even start exercising. So I would say 30 minutes a day is a minimum if you’re serious about starting to build your muscles.

Effective bodyweight workout routine

Easily. You could easily build muscle with 5 minutes. The key variable is intensity. If you go as hard as you can as if you had to do max reps for push ups in 20 seconds but maintained that for 5 minutes, I guarantee you won't even reach 5 minutes. All you have to do is just increase the intensity

If You’re Some Kind of Genetic Freak - Sure

Everyone else needs variable stimulus to elicit a hypertrophy response but in general it’d be around 30 mins of intense lifting.