Advice needed for a LED Strip Fuse Box

Nope, you want an IRL (logic level) type and probably 100A as in the board I referenced. If you look at the gate-source voltage against current chart in the data sheet, it isn’t fully on until about 8V gate-source and you don’t have that much drive voltage. The 100A rating typically doesn’t cost that much more and reduces RDSON (to reduce IR drop at 100A) which helps you even at 5A as a lower RDSON reduces the power due to IR loss in the MOSFET. That is more important for your application than switching losses as you aren’t switching. I have to go out for a bit but I’ll have a look at what I’d suggest a bit later.

Peter