Dont know if my puppy has had its first shots yet?
It does not matter if shots a repeated , if you have no record any reputable vet will give the first seires of shots unless you have proof that the pup has already been inoculated already.It really is no big deal but he does need to go in because at 4 months he will have to have had a rabbies shot and as you say he is already 5 months, he should also be started on heartworm Meds every month . Just be safe and now that he is your pup take him in and let him get to know the vet. He should need to be nuetered or (spayed) soon and will need a few other shots within the first year ………
If you know who the vet is, call them. If you know where she lives, don’t call just go over there and ask her. Be nice but ask for the name of the vet. Sounds like the pup hasn’t had anything. If she has been spayed, you should be able to see a scar in the middle of her tummy when you lay her on her back. Hold her like she was a baby and check her belly for a scar. If you don’t get the vets name or the records, make an appointment with a vet and take her in and ask about shots and if he can tell if she has been spayed.