The first point of your question is relatively easy to answer - points stay on your licence for three years. As the three points you mention have been on your licence for 5 years, you should apply to the DLVA for a fresh licence. The second part of your question isn't quite so straightforward. The Rehabilitation of Offenders Act 1974 enables certain criminal convictions to become 'spent' after a rehabilitation period. People often wrongly assume that the rehabilitation period is determined by the offence committed; it is actually determined by the sentence received. There are difference rehab periods for those under 18 and those over 18, but I'll give you examples that apply to the latter - prison sentences of 6 m or less - 7 years; prison sentences of between 6m and 2.5 years - 10 years; fines, commuinity service, probation - 5 years. So, for instance, if someone convicted of drink driving received a fine, the rehab period would be 5 years, after which time their criminal record would be 'spent'. (In this instance, the motorist's driving licence would be endorsed, which would last for 11 years.)