Downsides of using 5mm fuses in 6.3mm sockets
The main things for safety are the interrupting capacity and the voltage rating. If you are sure that the replacement meets or exceeds the original specification, you should be okay. 

Presumably this is to replace an ABC style fuse. 

This type of fuse is not considered safe under IEC 61010-1 for use on equipment directly connected to the mains (Cat II and above).