Hi.
Firstly, I recommend you check entry requirements for the courses/degrees that you're interested in. I don't know much about bio-mechanical and electrical engineering, but my concern would be that chemistry would be more important/valued by unis than further maths. Do check entry requirements, though, as I'm not entirely sure about that.
Secondly, four A-Levels is really the maximum that sixth forms and colleges allow for a reason. Any more than that is an unreasonable workload in one sitting, especially when considering that universities only require three A-Levels. The jump from GCSE to A-Level is a lot, so be cautious at the very least about this idea. If you're determined to do five A-Levels, talk to your teachers about workload, ask questions, ect, and keep an open mind that it may be too much.
I hope this helps, and if you have any more questions, feel free to ask me. 😊