Peanut may be right in that the inrush current is causing the fuse to blow.
42 inch LCD TVs are rated at around 200 � 300 Watts and therefore should be drawing around 1Amp. A 5Amp fuse can pass over 7Amps for short periods without blowing � which would lead me to believe that you have an intermittent fault within the TV.
The TV will have internal fusing, to protect it from a large fault current, however this fusing is often after the mains filtering within the TV. It is possible that there is a fault within the filter components (or somewhere else, before the internal fuse).
Unfortunately if this is the case � I do not know of an easy way to prove it.
You could try fitting a 10Amp fuse, if this blows I would definitely have the TV checked out.
I might even consider unplugging the TV at night.