How long can you leave beef shanks out to cool before refrigerating?

Braised beef shanks (not the whole shank, about 5 pounds of it cut horizontally like oxtails) all night long (12 hours), now I'm pressed for time. If I leave them out for 5 hours is that too much? I get mixed info ie: allow to cool thoroughly before refrigerating, or don't leave out for more than two hours. I have a cool kitchen, about 65* F. I'm just really perplexed over that. I only have an hour to let them rest or they will have to be out for a total of 5 hours while I do a volunteer gig for the NPS. Any tips? Grass fed beef shanks do not want to waste or spoil the taste.