5 days in the fridge is tops for me, although I've heard others go as long as 7.

To maximize fridge time, an important thing to do is to scrape the slime layer off the fishes skin (if you don't remove the skin). The slime layer is a haven for bacteria and it will accumulate, shortening fridge life. Simply take your fillet knife and scrape along the skin starting at the head and moving to the tail (opposite way of scaling). Rinse the accumulated "snot" off the knife before making another pass.