Fuses are not very precise things and different types have different characteristics.
The ideal fuse will carry rated current indefinitely but will blow sooner or later above nominal rating. Your 80W panel under some conditions could exceed 5A but would be within the rating of most 5A fuses.
There is no chance of the fuse protecting a panel so as long as the fuse can protect the wiring then it will do it's job. In this case increasing the fuse rating to 10A will still protect your wiring if you have sized for sensible volt drop.
A decent quality industrial HRC fuse rated at 5A would have handled that load indefinitely, but many of the cheaper fuse types age and fail even at nominal rating if there is a long enough period at full rating.
In high voltage systems there is a lot more latitude and fuses can be sized considerably above normal load rating and still clear a fault quickly. With low voltage things there is less margin as the cable resistance reduces the fault current but in most cases using a fuse rating double the expected current is usually ok. You have to be very cautious on long cable runs but for inverters and similar on thick cables you need a fuse about double the expected current to avoid false tripping .
If you are using car type fuses they seem to blow very easily with even the slightest current over nominal.
If the thing blows a 10A fuse then something has gone wrong with the panel or its associated diodes .
Flux
