No, it's not a cpu bottleneck.
I have the same slowdown. Increasing res, increases fps. This indicates there is not a cpu bottleneck.
If it was a cpu bottleneck, fps would be the same if you increase res.
There is a similar thread where the RX 480 is experiencing this slowdown and nvidia's card is not. This is not a new issue with the 5700. It was a problem with older cards, so there is something amd driver team really needs to look into. This problem will continue to repeat with newer video cards.
It's not specific to Crysis 3. But it seems like an issue with older games that the card thinks is less demanding. Maybe there should be an option to have full clocks while gaming instead of the aggressive core throttling.
I went with AMD because of that fine wine technology. AMD, please deliver!