Why would a 5 month old pup need 3 set of shots (never had any)?

They give three sets of shots because they have to build up the immunity gradually. If they give them to much at once the pup could get very sick. I am more concerned as to why a 5 month old dog was never vaccinated in the first place and that the place she is getting the dog from has not started the series of shots. I would never bring a dog home that had not had the first series of shots as I would hate to bring something into my home to hurt my other animals.