Hi @Sienatulipa that definitely doesn't sound right. We're on about £7 a day this month, up to £10 yesterday but it was below freezing all day, we're in a 4-bed detached.
Hard to understand what the reason for your high electricity use is but things to ask the installer are:
What is the flow temperature (ie temperature of the radiators)?. It may be that if your house is getting cold, it is set up to try and heat as fast as it can, and so running inefficiently.
You need to have it set up so the flow temperature is always low, even if that means running the system for longer. If you allow the pump longer to put the same amount of heat into your house it will be cheaper.
The pump might be 'cycling' so ask your engineer about that. Cycling means rhe pump pushes out hot water faster than your house can cool it down and it is still warm when it gets back to the heat pump, so it turns itself off.
It can a be a problem if the pump is too big for the system. Do you know what size the pump is? For a normal sized well insulated house it should probably only be 5-6 kW. If you were sold a bigger one that might be causing problems.
Alternatively if the pump is too small (unlikely) it may be using a supplementary heating coil to try to warm your house up quickly. You need to ask this too!
The other thing to ask about is the hot water. It is much more efficient for the heat pump to heat the tank to 48 or so degrees than the usual 60 or 70, so the tank should have been sized to allow that. Ask the installer what your hot water setting is. If they have set it to 55 or 50 that will be costing extra money too. I assume you do not have an immersion heater connected? If so, check it isn't coming on.
Most installations then run a 'legionella cycle' to heat up the t ank periodically to kill any germs. No-one really knows how often this should be done, but if yours is happening wekly that is probably a waste. Monthly should be more than frequent enough.
Lastly your bills should drop significantly as the weather gets milder. So if it's 10 degrees outside not only does the house need less heat than when its 0, that heat should be about 25% cheaper, so your bills should very much be weighted into the coldest weeks if the year . An estimate of £5k is averaging £400 a month right across the year. Unless you are also running a hot tub you haven't told us about, I can't believe that youll be using that much in the summer especially with solar.
(Unless the engineer has done something really stupid and somehow got the hot watertank heating the solar panels and the sky...🤷)