What can I do to stay focused when compiling? What do you do to solve this problem?
Get compile times down to more reasonable levels. Use the shorter breaks for checking on things in your issue tracker to start on whatever is next in your queue.
You can also listen to Lord of the Rings on audiobook[1] to occupy your mind while you wait. You're probably familiar with the storyline, so you don't have to worry about missing something important when you aren't paying attention to it. Trying to make that time productive is going to lead you to feel frazzled as you keep context-switching.
[1] http://www.audible.co.uk/pd/Classics/The-Fellowship-of-the-R...
It's a good time for a trip to the restroom or to refresh your beverage, but you can't do that every 5 min.
I'll often deal with email (our issue tracker sends email for comments, so there's usually something to deal with there) or catch up on slack.
There's always something that needs code review.
I'll check some monitoring dashboards for servers I'm responsible for.
And I have project management responsibilities along with the code-related ones, so I can take care of some of that.
Of course, all of those other than the first require significant context switching, but so does reading HN.