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