5 month Tibetan Terrier getting wild when out of his cage...

Sounds to me like a pup that needs more exercise and socialization.  Instead of just "taking him out of his cage" how about open the door, carry your pup outside to do his business, reward and then a little playtime?

At 5 months he's got a whole lot of puppy left in him and if the rules weren't firmly established and enforced, then it's time to do so; in a consistent and fair manner. 

Has he been to puppy class?  Basic obedience?  What kind of food is he being fed?  How long has he been in his crate?  Does he have any chewies or toys in the crate with him?

There are a million variables but it all adds up to YOU, the human, need to assess your tibetan's needs and supply them, whether those needs are exercise, structure, toys, better food, or more socialization.

HI -- what you're describing is a very normal, healthy puppy -- a pup should *only* be crated when absolutely necessary -- like if you MUST be away to work, or during the night when he can't be supervised.  BUT a puppy can not be crated 'most of the time' -- they literally are non-stop play machines and the reality is, they must be played with and exercised for hours a day in order to wear off that puppy energy, help them grow and develope normally.
 
What Xerxes said is absolutely true -- now rather than just putting the dog back in it's crate after it relieves itself, try leashing the dog TO you.  Put a 6' leash on and put the handle right over a belt around your waiste -- that's gonna help keep the dog close but give you hands-free to do other things - but you gotta watch them and play with them ALL the time.
 
A tibetian spaniel is quite a high energy dog -- they tend to have very independant personalities and are very smart -- if you don't develop that personality and help the dog learn how to play and how to defer to you (ie.., you be the 'alpha' and teach the pup TO please you) then it's going to grow up wild and uncontrollable.
 
Perhaps you aren't an experienced dog owner (and I'm not sure I'd have told you that a tibbie was the right dog for an inexperienced owner) and perhaps you've never had a pup before -- but they are a LOT of work and not just for a couple of months.  A "puppy" is truly a puppy for at least TWO YEARS.  It's constant training and frankly at 5 months you are only *beginning* to see the independant personality emerge.  This dog is embarking on sexual maturation and that means it's a bit like a human teenager -- they will push their boundaries and limits and that IS NORMAL.  It's part of the growth process.
 
Maybe a schedule will work -- and set a timer so from 5 - 6:30 it's A's responsibility and then 6:30 - 8:00 it's person B and then C gets 8:00 - 9:30, and then maybe back to A.  Rotate it off so everyone gets/needs to feed and do training. 
 
Puppy classes are a must -- that helps not only teach the dog, but more importantly it teaches the HUMANS **how** to teach the dog.  That's not 'natural' for anyone -- I always encourage whole families to take obedience classes simply because learning TO handle a dog is half the battle.  Learning to set things up so you CAN win and get the dog to do what's needed is important.
 
Every time the dog successfully is a little stinker -- every time he 'escapes' and does something naughty -- he's learned something.  He's learned HOW to get his own way.  So if you call him and then don't follow thru and make sure he comes ... you've taught him you don't mean what you say!!  Getting the whole family educated isn't easy -- but my guess is that at least most of the family **wanted** this puppy before you got him. 
 
"But it's NO FUN anymore!! He's a pain!!" -- so you say to the rest of the kids -- "You know what?  Sometimes YOU are no fun and YOU are a pain.  Sooooooo does that mean I'm supposed to keep YOU locked in your room all the time???  Probably not.  Does that mean it's ok for the rest of the family to ignore you?  Nope.  WE got this dog as a family -- so WE all need to train him.  And just in case you're wondering -- ALL puppies are a lot of work, but they aren't even the beginning of how much 'work' a human child is .... so learning to deal with this dog's needs is just plain good training for life.  ummmmmm get RID of him??? Well, we're back to what I said before -- sometimes YOU guys are no fun ... so ....which one of YOU do we vote to get rid of???  I didn't think so.  We committed to this pup so WE need to care for him.  So .... who wants sthe first shift tomorrow???"
 
I'm not trying to be sarcastic -- but I've counselled a lot of families thru "puppydom" and usually it takes everyone realizing that a commitment IS a commitment -- what sounded easy and "cute" is now work.  But it will pay off. 
 
You may want to get a small carrier -- so that you can keep it IN the car -- and if there are tons of after school activities and running around -- keep the dog WITH you -- teach it to be a good rider and it gives him the opportunity to get more socialization that way.  Yes, it IS work to take them with you -- but eventually you will get a dog who is great at being "portable" and who learns to adapt to all sorts of situations. 
 
Tibbies are awesomely smart dogs -- but they'll think beyond you to 'manipulation' in a heartbeat.  Don't let it happen.  Nothing 'good' in this world is ever 'easy'.  But neither is it intuitive to know *how* to do this kind of training, so you all kinda have to learn together.
 
Stuff to read:
 
Dr. Stanley Coren's "How to Speak Dog"
Carole Lea Benjamin's "Mother Knows Best"
Dr. Nicholas Dodman's "Dogs Behaving Badly"
 
GREAT internet research:  cut and paste this into any search engine:

"Nothing In Life Is Free" dog training
 
Have fun!!

I agree with what Callie has said.  Also, if you have any friends who also have pups of a similar age, maybe he can do a "play date", or if you have dog day care, or a dog walker service in your area, that might be a temporary way to tire the little guy out.  Puppy owners have a saying - "a tired dog is a good dog". 
Puppy class will teach you how to teach him the skills that you can then use to tire him out mentally, as well as physically.