Is it unhealthy to ejaculate more than 5 times a day?

Seems more. than most people. Doubt any adverse physical problem but it may be element of addiction or use as therapy for underlying depression and anxiety.
Here are some ... If you can keep up doing a good job in effectively handling personal and occupational chores and tasks despite ejaculating >5 times a day, that is okay since it's personal matter. But, most men just cannot keep up with such obsessive behaviors because, in reality, ejaculation is a process of heavy mental and physical drainage. So, don't let obsession rein and ruin personal life.
Depends. Any behavior can be bad if it interferes with our normal functioning or gets us arrested. So as long as you don't miss work, school, or do it in public or with dirty hands and it doesn't interfere with normal healthy relationships or activities, no problem. This should not be your only form of exercise though and builds only a a couple of muscles. Too much of anything is not good, generally.
EJACULATE. Please find another hobby before you hurt yourself.