There is a level of judgment call that goes into this question, but there are also two metrics that are most telling in making it: how round the tire looks in profile and how much tread thickness is left in the contact patch when the unmounted tire is pinched between the fingers, relative to the adjacent sections. The view you present, of the tread surface not in profile, would be enough to make the call in an extreme case, i.e. lots of deep cuts, but as you say that's not what you're up against here.
5000km on the sort of tire you want to be racing on in the first place is pretty considerable, although that depends on what tire it is and rider weight/power.
I think the tire in the picture probably still has some life in it were the purpose to economize, but if the race is at all important to you, go in with a fresh one. As others have indicated, some kind of shakedown ride is good, but I wouldn't split hairs about the exact amount of break-in. (At high levels it probably is reasonable to worry about that and all other aspects of tire conditioning, but for most people it's basically go on 1-2 rides.)