5 hours in LFR and nothing to show for it

This is impressively bad. That’s a minimum of 36 pulls to clear six bosses in the story mode of WoW.

Odds of loot are ~20%, and you killed six bosses. So one boss more than the average single loot drop. You got marginaly unlucky, it just feels worse because you had exceptionally bad groups that wasted a ton of your time. This shouldn’t have taken you more than an hour within the actual instances.