@jmel - I cannot get your screen name to prompt - so apologies that this isn't immediately sending your way. Is this your first year with the Marriott card? If so, you should call Chase to ask what's going on with your 15 elite nights credit.
However, my initial thought though is that you are in year two or beyond, and you have not yet hit your anniversary date. I suspect the 13 nights you see are Rewards Credit Card nights tied to your spending (every $3,000 spend earns you another night). When is your anniversary date? Have you hit that this year? This is fresh on my mind, because I just hit my anniversary date this week, and my Rewards Credit Card nights total jumped 15 this week.
It's possible you have the Marriott Rewards Credit Card instead of the Marriott Rewards Premier Credit Card. This card offers 10 elite nights credits, plus 1 for every $3000 spent. The Premier Card does grant 15 nights, plus 1 night per $3000 spent.
Check out the differences
If this is the case, you might try contacting Chase to see if you can upgrade to the Premier card. If so, I'd also ask if they will credit you the 5 additional nights.
When I read this @jmel I immediately thought either nights for spend was crediting separately from annual nights, or wrong card, but as both bejacob and nationwide have identified both these possibilites (clever chappies) I'll just reinforce what they say, that it's most likely to be one of those two!