It is almost like they calculate electric heating/cooling all year round. Crazy. As you say my home is huge, at least 500m2 of rooms which must be run. I run a bunch of computer equipment, my pool is running 2 hours a day. Currently we have 3 fridges running and 3 freezers, two of which are chest freezers. We also have a water boiler in the kitchen. This runs away with about €40 a month and I have it on a timer. Hot water is also electric and for the two of us I have it down to 1h per day which normally suffices. I ramp that up to 2/4 hours per day depending on how many are in the home.
My costs won't reach this. OK French electric is cheaper than the UK and I don't use gas, but, honestly, I'm in the Upper range for energy usage. I normally only use fans in my office but this year I've a small portable aircon unit in the room. I expect that will bump the cost a bit.
Where this £5k a year is coming from I don't know. Apart from, political attempts to motivate the government to provide funding to had off future pain.