Once in a while we see persistent sneezing because there is a foreign body in the nasal passages. We have found a piece of thread, a piece of ribbon and several blades of grass on exams over the years. Also, periodontal disease is reported to make some cats sneeze but this seems pretty unlikely in a 5 month old cat. Rhinotracheitis is very easy for cats to pick up prior to being successfully vaccinated against it. It is probably not possible to protect all cats, even with vigorous effort.
Allergies probably do cause some of the sneezing seen in cats.
Your vet can examine your new kitten and rule out some of these causes. My question is, he has sneezed since the time that I found him. He sneezes probably once every hour. Otherwise, he is very healthy. He has a shiny coat, plenty of energy, and is perfectly healthy, other than the sneezing.