It may have been a shorted socket that caused the original 5A fuse to blow, but it could have also been coincidence...

Slow-Blow fuses are designed to blow eventually, regardless of there being a problem or not. This is due to their design - they can handle more than their rated current, but only for short periods of time. The more often a slow-blow fuse has to handle a higher than rated current, the less time it has before blowing.

You can use a higher rated fuse in this case, but do not use it permanently... ie: use a 6.3A slow-blow fuse and see if it blows reasonably quickly. If it does, then you do really have a problem, and a 5A is not gonna last long! If the 6.3A lasts, then you have probably already solved the problem.

I wouldn't go any higher than a 7A fuse just in case, and do make sure you put the correct fuse in ASAP. There are only a few instances where you can get away with a higher rated fuse for testing only, and this is one.