I'm glad you have a vet appointment-- it's unusual for a 5 month old kitten not to want to play, and the sneezing would make me suspect an upper respiratory infection. URIs are really common at most shelters because there are lots of pets in close quarters and the stress of being in a shelter can inhibit their immune systems sometimes. If your vet tells you he has a URI, it might be a good idea to give the shelter a heads-up (although I think most are kind of always on the lookout for the symptoms in pets since they're so common). Most likely you'll get an antibiotic and he'll start feeling better within a couple of days. I was on the board of a rescue that pulled pretty much only kittens who were sick with URIs straight out of their isolation ward, and most cleared up really quickly (one or two just needed a different antibiotic than the one that was given originally). The antibiotic combined with the lessened stress of living in a home can do wonders for them.
#PetHealthandNutrition