I'll chime in and say, despite the naysayers, I noticed shifting was markedly improved when upgrading to 5800 from the previous generation of 105 (5700), particularly the amount of pressure you had to put on the front derailleur. If you are coming from 4600 Tiagra, I would say it would be worth doing if your chainrings, cassette and chain are worn out. If you are already on 4700, stick with that though, as I hear that's better than the old 105, so you won't benefit much from the upgrade. You might have to factor in the cost of a new wheel to upgrade to 11 speed if your hub isn't compatible with the 11 speed cassette.
Upgrading will not make your faster, it's not as cheap as replacing the worn components like for like either.