Why are my beef short ribs still chewy after 5 hours? In short:  

Kamado at 250-275f
Short Ribs in for 4-5 hours  

The ribs have a layer of meat, then a small layer of fat, and then the meat on the ribs themselves.  The top layer gets reasonably soft and edible, but the main chunk of beef is much too chewy still.  

I've had two goes at this, the first time the temperature was closer to 300f, and a bit shorter cooking time.
In both cases, I stuck a toothpick in both parts of meat, and it went in as if the meat was soft and tender.

Basically, what am I doing wrong? Not enough time? Not enough heat?  I worried that I might overcook them and dry them out. So I might try again, but wrap them in foil halfway through...

EDIT: What I did that worked
First of all, it's a shame that I can mark both answers as answers, because they both helped.
What I did was to smoke the ribs at 270-285f for 5.5 hours, and they were bloody perfect.
I started at 270, and opened the bottom vent enough that the temperatures slowly went up to 280 over those 5.5 hours.
Thanks to everyone for the help.

Edit: And thanks to the user who edited my question and made it worse.
At least learn grammar first, and maybe contact the person asking what their intent is.
There is conflicting information on the Internet about BBQ short ribs,  so, I can see the confusion.   

Serious Eats suggests that you want to grill short ribs to an internal temperature of about 130 F (54.5C) (medium-rare).  They suggest that any hotter, and the fat will start leaking out, drying the final product. Short ribs, grilled in this manner, are common in Argentinian and Korean cuisines, among others.  

I see that your approach was different, going the low and slow, BBQ route.  There are folks who use this method as well.  

The Big Green Egg forum has several examples. Almost all of the low and slow recipes that I see employ the "Texas crutch"; that is, after a couple of hours of smoking, wrapping the short ribs in foil with some liquid, and returning to the smoker.  The Texas crutch helps control moisture loss and helps with tenderization.  This is probably the route you want to take.  

If you have the proper equipment, a third approach I have used with great success is to first sous vide the short ribs.  That way, I can cook to medium rare, for as long as 48 hours (greatly enhancing the texture), and finally tossing on the smoker or grill for a much shorter time to add the smoke flavor and develop a crust.