Are Shimano 105 R7000 STI levers compatible with the older R5800 deraillers?
Short and easy answer - yes.

Shimano compatibility charts show ST-R7000 shifters are compatible with FD-5800 front derailleur and RD-5800 rear derailleur. All Shimano road rim caliper brakes are compatible with each other.

http://productinfo.shimano.com/#/com/3.7?cid=C-453&amp;acid=C-455