Are 105 r5800 front derailleur and Claris rear derailleur compatible?

Problem with 5800 front derailleur is that it's an 11-speed front derailleur.

Usually you can mismatch by a generation with front derailleurs, so that 8-speed and 9-speed can be interchanged. But in this case you would be mismatching by three generations.

I suspect the 11-speed front derailleur is made for far narrower chains so you'll have a terrible front derailleur chain rub. With friction bar-end or downtube shifter, it might be tolerable by trimming the front derailleur, but if you use indexed shifting for the front such as STI levers, you will have a very hard time trimming.