Hi sarah. SBTs are, apparently, full of beans! But yes, that applies to most dogs. As has been advised, his walkies should be built up gradually, at 5 months he is young and you don't want to damage his bones and muscles, as they will develop until he is 18 mths-2 yrs (maybe others can give a more exact age?) Take it slow with him for now, and keep an eye on him. He should be allowed to stop if he's tired out (I know, sometimes it feels like he never is!), so he shouldn't be forced into carrying on walking. Walks round the local area to get him familiar with his surroundings, and meeting other dogs will be valuable.
As for the mouthing, you need to be really firm with him. If not, he won't realise the damage his bite can do. This is potentially dangerous, esp. with a dog like a Staff, which has a lot of power in its jaws. If he mouths at you in play, yelp as if in pain, or say NO v. firmly, and after that, stop any interaction with him, and ignore him until he settles. If he does it for attention in everyday situations, do the same. You need to give him NO reward for his behaviour, and that includes your attention-even negative attention can seem a good thing to a dog. Make sure EVERYONE who spends time with your puppy follows this, no-one can be lenient with him because he's "just" a puppy. They'll regret it when he's a fully-grown dog.
Stick with it, it's so worth it to have a dog that is happy, and healthy, and that you'll just love forever! Good luck, let us know how it goes. x