Is the Series 5-7 Story Arc Actually Explained?

Short answer: Series 6 & 7 are explained, Series 5 isn't. We finally got an explanation of what's so important about the Doctor's name and how Clara could be in all those places, but no explanation of why the TARDIS exploded.

Since the Doctor's name apparently unlocks his tomb, it appears the Silence didn't want anyone to have access to his timestream. They didn't want anyone to have the ability to go in and alter his life. This would almost make it appear that they are the good guys and didn't want anyone to unsave everyone he'd saved. Another possibility, however, is that the didn't want anyone to know about the Doctor's other regeneration. I don't get the problem with knowing, so there's the possibility he's trapped there and is somehow going to escape. He was the only regeneration who actually interacted with Clara and the Doctor. The others all just ran about completely oblivious to them, he was somehow different.

Clara's mystery did turn out to be precisely what some people predicted. There were a number of theories going about how she was splintered in time (similar to Scaroth in City of Death), however, no one seems to have gotten how she was splintered. She shattered herself across the Doctor's life in order to save him at certain key points. It's interesting how we didn't see her saving the ninth or tenth Doctors at all, I think they're saving footage of them because they're going to be appearing in the 50th anniversary.

Two seasons & three years later, we still haven't received an explanation of how the TARDIS exploded. I think we're being led to believe that the Silence did it, but it's not entirely clear. We've received no motive on their part. If they're trying to kill the Doctor, then they're smart enough to realize the effects of blowing up a TARDIS and should really have been able to realize that he wasn't even onboard. I'm still holding onto the theory that the Time Lords did it to execute the Ultimate Sanction since I haven't seen any evidence to the contrary.

I guess Moffat must be saving his explanation of the TARDIS exploding for the 50th anniversary or Series 8. That may actually be separate story arc that has nothing to do with the Silence or the Question. He may simply have planted it so long ago in an effort to keep us watching so we would sit through Series 6 and 7 before finally finding out what happened. He must surely know from the internet that we don't have the foggiest idea, so he's got to explain it at some point or another.