If you start taking birth control 4-5 days before your period is expected will that stop it from coming?

Probably not that quick, it takes a while for your body to recognize that correct level of the horomones in Birth Control to regulate your period, this as well is why you would no be protected from pregnancy that fast either. Depending on how regular your period is, it may even take a few months for it to come or not come exactly according to your pill schedule.

Could do but not definate. You can however get tablets from your doctor which can stop your period coming for a few weeks. I got them last year, you need to take them 7 days before your period is due then stop taking them when you want your period.