My App Store refuses to Download and Install the MacOS upgrade from 10.10.5 to 10.11
You have to go through the App Store to get to 10.11 (technically not true-- you can buy El Capitan on a USB drive, for example). What I mean is you can't just go to apple.com and search for El Capitan and download it. After you have some version of 10.11, you can apply the 10.11.5 Combo Update (although you will not have to since you will get the latest, freshest 10.11.x from the App Store and that's 10.11.5).

The 10.11.5 combo update is for taking a 10.11.x system to 10.11.5. It won't work on 10.10.x. So you are doing the right thing going through the App Store, but I think something is clogging up the download-- probably an older software update that didn't complete.

Look in the Purchases section of your Mac App Store app. You may have an older OS download that is stuck (or paused) too, in addition to the El Capitan. Maybe Mavericks, maybe something else. If you click "Resume" on that one I think it will simply disappear and your El Capitan will resume instead. I Basically you have to get rid of the OS download that is clogging up the works. You may be surprised to find such an old and incomplete system upgrade in the Purchased section-- I was, when it happened to me.