Cows milk is very hard on the stomach and usually causes diarrhea . If it had any,give it some pedialite through an eyedropper or syringe.about 5 ml 2 times will replace the lost fluids. Also a drop of honey will give your cat an extra boost of natural energy- these are things i learned from my vet ,since i raise kittens!!!
The best milk ,if you cant find kitten formula -is goats milk 2/3 and 1/3 water
since your kitten is already 5 weeks old ,it could eat from a tiny saucer,mix the milk with baby cereal to make a soft mush
after it has gotten used to it ,in a eek,get proplan kitten can food and ad a tiny bit to the mush ,increase this and the stomach will get used to it.if your kitten stays this limp for another day ,and it wont perk up -carry it to the vet for a check up!! Good luck

 Have your kitten checked out by a vet, there may be something wrong with it. I am not saying there is i am just saying you don't want to think it is something and you find out it is something else when it is too late.