You can not expect a 5 month old puppy (or a puppy of any age) to know the difference between the right thing to chew on and the wrong. I used to teach obedience classes and what I always told my students was, no matter what they chew up or pee on, you can't blame them... You should have been supervising in the first place. Think of it this way. Would you give your 2 year old child a magic marker and then turn him loose in an house that hadn't been childproofed? Bad idea.
With that being said, there are two things that need to happen. First, he needs to always be supervised. ALWAYS! If you can't watch what he is doing he should be in a crate, or outdoors (if you don't mind the fence being chewed). When he is inside with you, you should reward when he chews on the right thing and redirect when he chews on the wrong. By redirect, I mean use something to startle him from the behavior (like clapping, growling, stomping... not hitting) and then give him his toy.
The second thing that needs to happen is he is probably quite bored. You say that he is very smart, but you don't say anything about formal training. He needs something to keep his mind active. Another saying I've always used is, "if you don't give your dog something to do, he'll find something on his own, and you probably won't like it!" teaching a trick here and there is not the same as participating in formal obedience or agility training.
Ah, I just noticed that you have a female... Sorry, change everything above from he to she ;-)
Feel free to contact me if you have questions.
Good luck!
A.
Mom to two boys under the age of 2 and many dogs (some with titles in obedience, agility, and conformation!)