So, a friend gave me there old DC05 because it was stopping and starting intermittently and they knew I like to problem solve.
I have cut some of the power cord and put a new plug on. Still the same problem. I have cleaned out the filters and got rid of hair from the cyclone.
After investigation on various sites I have discovered that it might be the thermocouple, which would make sense if it is overheating. On a DC05 where is the thermocouple and how dangerous would it be to bypass it? Also, if I pick up a new motor on ebay will that include the thermocouple, as one person I read changed their motor but still had the same issue.