You'll need to read the spec of the fuse. Fuses have time periods over which they'll sustain a given current. In the case of bulbs, there will be a higher current when you switch them on (until the resistance of the bulbs increases as they get hot), so you'll almost certainly likely burn out a 5A quick-blow fuse if it is 5A during normal operation.
Fuses are coarse devices that help prevent (but do not prevent) further damage and safety issues in fault conditions. They help cut power under conditions of gross faults. For smaller ground faults that might not blow a fuse (e.g. you can't use fuses as a means to prevent electrocution risks), you need a RCD type circuit.
Personally, I'd likely use a regular 13A slow-blow fuse for 5A worth of bulbs, unless there were some other sorts of high value circuitry attached that had some specific need for something more exotic to protect them.