If those are stats for Aqua:
CPU total - 5m 5s
CPU foreground - 3s
Keep awake - 8m 32s
I'd say it's not bad -- 8.5 minutes of "keep awake" time over what, 5-6 hours? Just two minutes an hour, or about 30 seconds per each mail check (every 15 minutes, even if that's not all of your accounts).
And definitely 8-9 minutes of "keep awake" should not be getting your phone from 100% charge to 20% in 5-6 hours.
Don't know what "screen off" vs "screen on" refer to -- must be something specific to your device's system software -- but I assume it's the app's battery use further broken down to when the screen is off vs. on. It's natural that the "screen off" portion would be larger.
What are the detailed stats for Google Play Services? What about other apps listed on that battery screen?
On my LG G3, before it got 5.0, I would get about 30% battery use by "Android OS" and "Android System", IIRC (and nothing like that on other phones wht 4.2-4.4)...
Sorry I didn't just go "aha, it's that checkbox over there, turn it off", but... the "keep awake" really does look quite reasonable.