Can A Kitten Leave There Mother At 5 Weeks?

They usually can survive if they're taken away at five weeks, but taking them away that early is not recommended. Their mother's milk has antibodies that help the kittens fight infection. If they're taken away too soon their immune system won't be fully developed, and they won't have the help of their mother's milk. That means they're left completely vulnerable. So kittens should ideally be left with their mother until about 10-12 weeks.

If the kitten has to be taken sooner or if the mother dies, you would need to keep a very close eye on the kitten. At five weeks their teeth are so little that it can be difficult for them to eat enough hard food to get the nutrition that they need. Most post stores sell kitten formula. A warm saucer of that would be best to start. Over the next few weeks, I usually move the kitten up to watered down canned food, then dry and canned food mixed, then just dry.

Five weeks ago we took in an approximately three-week-old kitten that had been found in a dustbin.  We bottle-fed him with special kitten formula milk.  Within a week he was nibbling at meaty kitten food and drinking milk from a saucer.
He very quickly learned to use his litter box and wash himself, and seems in perfectly good health.  The only problem that is possibly associated with leaving his family too early is that he bites and claws too much at any bare human skin!
One mistake I made was, that after keeping him in a large cardboard box for the first few days, that he soon escaped from, I realised that I hadn't given him enough "shelter" within the box.  Once given the freedom of an entire bedroom, he always chose to sleep in a cosy corner that had a soft "roof".  So if you keep your young kitten in a large box, give him also something like a smaller box turned on its side with as much softness as possible all around.  
Kittens of such a young age also need to be kept very warm - around 26 degrees C.  A well covered hot water bottle could do the trick.  We got Figaro when the outside temperature was around 35 so no problem for us!