Why would you need a 5 A fuse in the FCU assuming the plug of the TV already has one fitted and the extension lead is suitable for 13 A?
Of course there‘s no need for a larger fuse but I can‘t see any reason to replace an existing 13 A one.
The fuse could be 13A if the extension cable is 13A rated.
Alternatively a less chunky 5A rated cable could be used if a 5A fuse was fitted.
But both are botches anyway, the sensible solution is just to chop the plug off and wire it in, as has been done already.
My point is to check that the fuse is 5A if doing this, the likelihood is that it has the default 13A fuse. The cable supplied with the TV definitely won't be 13A rated, more likely 5A, and possibly even 3A. Check the writing on it and fuse accordingly. It may not state a rating but just a code, in which case google will tell you the current rating.