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.
The reason it is suggested that you let hot food cool before putting in the fridge is to make sure the overall temp of the fridge isn't reduced, thereby protecting all of the rest of the food. I would let them sit until the last minute, then put them in the fridge just before you leave. I am uncomfortable leaving food out for the 5 hours you mention.
When you put them in the fridge, make sure the container isn't touching any other food so that food doesn't warm up!
Just as you can thaw frozen items many times faster in a water bath versus air, you can cool things in a water bath faster than you can in the air. Let cool slightly in air, then put your dish in a tray of water, and let your faucet continuously cool it. You can get it in the fridge faster this way.
Worth pointing out that this method is the best way to handle raw milk, cooled quickly in a ice water bath before putting it in the freezer, minimizes the time it takes to get cooled below the temperature where bacteria thrive. Body temperature milk takes some 8 hours in a conventional fridge to cool to fridge temperature, at least in my experience and fridge.