Three points I'd make are:
- 5km rides isn't a lot to keep the battery charged. You should budget on buying a charger and giving it an occasional long (12hrs) charge up. Occasional means "a couple of times in the winter" in this context.
- An alternator problem could be exacerbating your problem, so is worth checking
- That's a heck of a drain on the battery somewhere. Since you've changed the battery, we can assume in principle that it's sound. That seems to be your root cause, and you'll have to go through a methodical process to identify the problem.
As Ffoxy says, the usual suspects are ICE and boot lamp (but normally neither would be this bad). So with the good weather I think your best bet is to go hunting with a multimeter. First, stick the battery on a charger for as long as you can. Then get the multimeter (always handy to have one, cheap at Halfords), a mate and a pen and paper - to write down the voltages and test type.
Ideally, the multimeter would have crocodile clips which you can connect to either side of the battery.
Charger off, note the battery voltage with ignition key out - 12.8V is good, less than 12.0V indicates a tired or near dead battery.
Start the car. With the alternator taking the strain, the voltage should be >14.0V. Less indicates a dodgy alternator, or loose wires.
Now to find the drain(s). First, open the boot, and press the plunger switch (which should deactivate the boot lamp) and check the light goes out.
If that doesn't work, get in the footwell, and expose the fuse board. Key out of the ignition), remove one fuse at a time. Call it to your lovely assistant, who should note the voltage reading. Replace, and repeat for every fuse. One (or more) should show a clear increase in battery voltage (current flow reduces the battery voltage, so the step up indicates a larger current flowing - the bad earth you are hunting). Remember though, some things (alarm/immobiliser for example) are meant to remain running with ignition off, so a voltage rise doesn't automatically mean you've found the answer - check them all while you're wedged in the footwell.
Check the manual, which will tell you which circuit(s) have a dodgy earth. You now need to check all the devices on those circuits - pressing switches, disconnecting wires as far as you can, and reading the voltage.
With luck, you'll find the offending item. Strip it, check for rust traces in joints, WD40 on connectors, leads properly connected, etc.
With a good wind, you should find the root cause. Worst case, at least you can tell the gargae where the problem is.
