You are dealing with the 5A circuit - which is the lighting circuit only - nothing to do with any of the 13A wall sockets which are on a different circuit (or circuits) and a much larger fuse.
If you say the lighting circuits were OK, you switched off the dining room light, then the whole lighting went off, then it seems most likely that the bulb in the dining room went short circuit (though bulbs normally break when one switches them on, not off). Try taking that bulb out completely, renew the fuse and try again. If that fails, take ALL the light bulbs out that are controlled by that fuse, renew again and switch back on.
If the fuse now doesn't blow, progressively replace each bulb until you isolate which one is causing the short-circuit.
If the fuse now still blows with all the bulbs out, you will have to call out a comptenent person to faultfind for you as there is a short-circuit in the cabling or (more likely) in one of your light fittings.