Battery life difference for 5 GHz vs 2.4 GHz WiFi - which is better Are there any difference for phone battery life when connected to 5 GHz access points vs connecting to the same at 2.4 GHz?
The coverage issue will have something to do with power usage. 

When comparing 5 GHz battery drain vs. 2.4 GHz, a lot depends on the coverage you are in with respect to each frequency band. 

5 GHz (for the same power) lacks the range of 2.4 GHz. Objects (depending on material) can obstruct 5 GHz more than 2.4 GHz (sometimes not depending on material). 

So, if I get 3 bars of 2.4 GHz in the furthest away part of the house (the upstairs bedroom) but only 1 bar at 5 GHz, my phone will likely have more trouble keeping in touch with the access point and that translates to more packets exchanged, a slower throughput (and that means more on-time for your 5 GHz radio and the system generally), and this will burn more battery. 

If you have good 5 GHz coverage and 2.4 GHz coverage in the same area, using 5 GHz is likely as good (if not a bit better) as it will pull faster, then wind down vs. the 2.4 GHz. When coverage starts getting worse for the 5 GHz, but not the 2.4 GHz, you may want to switch to 2.4 GHz for battery reasons. 

Factors impacting your performance:


Distance from AP
Quality of your 2.4 GHz and 5.0 GHz antennas both in the phone and the AP (should be roughly similar but...)
Other nearby networks using the same 2.4 GHz or 5 GHz channels your devices want to use (channel contention and/or interference)
Other RFI (interference with the radio bands you care about - badly shielded microwaves or other energy emitters that might shed harmonics off into your APs radio bands)
What you are using your device for (the occasional short message or long many MB movie streaming) as this will emphasize or de-emphasize performance and coverage distances (two identical devices on different bands sitting mostly idle probably won't see notable battery differences, but two streaming hard most of the time may well see not only the difference in battery from streaming, but further degradation in charge based on if the 5 GHz is in poorer coverage)
Materials between your portable device and your AP


I'm likely missing a few other factors and how significant each one mentioned is depends a lot on the gear, the interference/contention in the area and the types of material, as well as the usage pattern for the device. 

But generally - poorer coverage -> more battery use, so if 2.4 GHz is showing more bars than 5.0 GHz, shift to 2.4 GHz.