Electrical – Is the RCD Breaker faulty

It doesn't sound like a short. It happens after five minutes... each time. To me it also sounds like loose wiring or a bad breaker. I would turn the circuit off and than I would visually inspect the back of the receptacle first. Are the screws tight? Any burnt looking wires anywhere in the box? Than if that is good I would switch that breaker out for a breaker that works. If it holds, you know your breaker needs to be replaced.

You must have confidence in knowing you know how to turn off circuits to do this. If you are uncomfortable, just call an electrician. I am sure it won't take them that long to figure it out. You could even have a breaker at home for them ready (and return it to a store- if they will let you- if he does not need it.)

Breakers and fuses are sized to limit the fault current that can flow. Each is sized to limit the current to that which the cable connected to it can safely carry. For example a 32A ring main circuit will protect a 2x 2.5mm2 cable ring circuit. Another example will be the 6A lighting circuits. These could be a single 1mm2 cable (though 1.5mm2 seems to be more commonly used).

You aren't expected to be running everything at capacity at the same time. Just because a circuit can supply a given amount of current doesn't mean that it will be doing. As long as the current draw at any point doesn't exceed the capacity of the fuse or breaker protecting it, it won't trip.

You mention 3A and 5A "plugs". This is the current above which the fuse in the plug should blow (at some point - fuses have different "trip times" for different overcurrent ratings). The appliance supplied by these won't normally draw the current marked on the fuse. For example if you had a 1W appliance, it would be likely to have a 3A fuse (the smallest common fuse for a UK 3 pin plug), but would only actually draw around 0.004A. You could technically therefore connect around 3000 of these 1W appliances through one 13A fused plug without a problem (practically however, you might find it more of a challenge...).

The important number to be considering is the total power draw (wattage) of the appliances in use at any one time, not the total of the fuse ratings.

In relation to you aquarium, as long as you don't overload the ring main, you'll not have a problem. If you total up the wattage of all your equipment, you can run approximately 3000W through one 3 pin plug. (Note though that it's common for double sockets to be rated for less than 26A, but it's not often marked on them). Your 32A ring main is therefore capable of supplying a bit over 7000W.

In the worst case, you could always have an electrician install a dedicated circuit to supply the aquarium equipment.