As most others have already stated, no 5 months is not too old and in fact, mouthing would naturally be at its peak right about now. It is not unusual at all and perfectly normal - he is still a baby and just in teething.
Since your post was titled "bite inhibition" I think it is an important point - bite inhibition as you already know is learning the strength of his mouth and how to use it properly - a puppy does not come into the world naturally understanding this and it only comes from practice, on a variety of objects, to learn. It is our job to teach a puppy what is appropriate to put his mouth on and what is not, but it is even more important to ensure that puppy has experienced putting his teeth on human flesh and understands the right strenght - or gentleness . This is right where your puppy is, so it is less about suppressing this behavior right now and more about teaching that it is hurtful, or too strong on human skin.
Mouthing, as common as it is, also varies by breed. I am one who believes strongly that mouthing is a bigger concern in some breeds than others. Those breeds with functions that are naturally supposed to be using their mouths, are usually the most mouthy of course. While I understand wanting to strongly teach a herding dog for example not to use their mouth (that IS a problem in that job), it is ridiculous to expect a golden retriever to NOT use their mouth - its instinct for them and a natural behavior for life.
You have one such breed - newfies often use their mouths to pull dingy pulls and rescue batons in their rescue work - to me, learning the strength of his mouth and then putting his mouth to good work by giving him batons and tuffy toys to carry/hold is a great outlet and good for teaching what to put his mouth on.....a matter or "re-directing" the behavior...not "suppressing" it in my view.