Is it safe to cook a brined turkey 5 days after taking it out of the bridge if it has been refrigerated the whole time?
I'm assuming you mean that you removed it from the brine 5 days ago but kept it in the refrigerator the whole time?
If you brined your turkey for at least 12-24 hours then removed it from the brine and kept it in the fridge...it should be okay to cook after 5 days. I wouldn't let it go much longer before cooking, however. Check to make sure that none of the turkey has any slimey parts and smell it. If there is any odor that is off...don't eat it. If it smells funky...it's junky. And if in doubt...throw it out.
A few years ago we had a death in the family that caused a delay in our Thanksgiving meal. My turkey sat in the brine for 5 days and another 2 days before cooking. Ended up being one of the best turkeys I've ever made.