There are two totally distinct possible offences.
1) Fail to have VED (tax). This is detected by the DVLA (from the continous licencing records) and prosecuted by them. if you have taxed your car on-line, the DVLA records will show the vehicle as having valid VED so no prosecution will follow.
2) Failure to display a valid disk. This is prosecuted by the Police and the offence is complete if no valid disk is diplayed whether or not the DVLA records show valid tax. Whilst DVLA state that you have 5 days, this is NOT enshrined in statute and you remain liable (although it would a jobsworth copper that pushed this for prosecution)