This is such an odd date and so here is the story dating back to 1582.
Prior to this time the tax year started on Lady Day, 25 March. Rents etc were all payable on a quarterly basis and some still are (I had to learn them all as part of my chartered accountancy training and I’m still waiting for them to come up in a pub quiz one day).
In 1582 Pope Gregory XIII moved the rest of Europe from the Julian calendar to the Gregorian calendar. However the British decided to do their own thing and stuck with the old calendar which left them 10 days behind the rest of Europe.
By 1752 this difference has increased to 11 days due to a difference in how leap years were recognised. Britain decided to make the change just 170 after their European counterparts. Keeping a 365 day tax year moved the start of the tax year to 6 April so the tax year has ended on 5 April ever since.