What a cutie!!! Thank you for giving him a good home. Poor pup to have been "used" as a gift, then rejected because of being an active, happy puppy. BIG surprise (NOT) that a working breed puppy is more than a five year old can handle. Were the adults really expecting their child to deal with the puppy on his own without the grownups stepping in and taking responsibility for handling, managing, supervising and training?
Anyways, he is with good people now.
As for his age, pups start to loose their puppy teeth around four months old, so the family you adopted him from could have been right about his age. Some pups are just smaller, grow slower, but are still within the GSD standard, and he may still catch up to an average size as he matures.
If he is healthy, happy, active, is in good physical form and eats and poops well, don't worry about his size of weight. In that pic you posted, he does look younger than four months and three weeks (so almost five months?), but I would use the start of teething as a good indicator of his actual age.
Good luck with him! Hope you stick around and share his progress!