Previous posters have already explained this, but to reiterate -
Your baby wanting to feed 5 -10 mins after a feed is normal (albeit frustrating!) Its called cluster feeding, and is part of the process of building your milk supply higher as they grow. So, you either feed more and get more milk, or top up with formula.
Some people never build milk production that high, though - I'm one who can't make enough milk for a baby, whenever I do.
So, feeding formula instead of indulging constant requests for more breastfeeding in a young baby will affect your long term breast milk supply and I guess that's what you relatives are fussing about. There is some evidence that the benefits of breastmilk are cumulative (the more they have instead of other milk, the more benefits it has for the baby.)
However, combination feeding both formula and milk is a perfectly valid and safe option. It also has benefits - mum can more easily get a break, baby is used to bottles as well as boob, you get the reassurance that they are getting enough food and hydration, they probably will sleep better...
Your choices are fine, and your relatives should butt out.