I'd echo much of what Andrew and David have said in terms of recommendations, but I think you're at risk of rushing/not making the most of being there, if you did try to do this in 4 or 5 days.
Based on what you've said, you're probably looking around 700 miles/more than 16 hours of driving, and that's only after you've got to Edinburgh, with another 800+miles (and at least another 12 hours) just to get to/from Edinburgh from Essex.
Given that, if I were you, and my break duration was fixed, I'd probably choose somewhere else - like Cornwall or Pembrokeshire - for this trip, given your start point. Otherwise, I'd suggest allowing a proper two-week window to do what you've suggested, and really make the most of it.
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