As far as I know (I just sell the things
) The fuse is there just to keep the sensitive internal parts from blowing, Same deal as not hooking it up reversed polarity.
To keep the warranty on your tiemr you must use this fuse. However from personal experience I know that these timers can handle more than 5 amps for some time without blowing. I have run one of my hunting decoys on a switch with no fuse all season long. The motor on this thing is a 28lb trolling motor unit. Draws a lot more than 5 amps and It still works.