PP, a Pandoras box you open perhaps? The 5th seems to be the prevailing wisdom, but Bill Sweetman in "The Great Book of WWII Airplanes" quotes both the 5th and 6th in different places.
From
Supermarine Spitfire - The Prototype - K5054
There has been much debate upon the exact date that this flight took place although the Spitfire historian Alfred Price uncovered a hand written report of the expenditure on the Spitfire programme dated 29 February 1936 amounting to £14,637 on which is hand written "flown 5 March 1936".
Bearing in mind that Reginald Mitchell was such a stickler for detail, and the fact that he would have attended the Board meeting on 2 April 1936 at which this certificate was presented, it can be taken that the Spitfire's first flight was on 5 March 1936 at Eastleigh. This has now been confirmed by the discovery of an original file, thought to have been destroyed, which reveals that the first flight lasted just 8 minutes starting at 4.35pm.
Some publications state the flight took place AM, rather than PM stated above.
"Spitfire - The History" by Morgan & Shacklady quotes the 5th. Quill wrote the foreward to the book, so one wonders how much attention he may have given to the content. The publication states the "Air Ministry Certificate of Design" was issued on the 6th March. Would this be issued pre or post first flight? Thinking laterally, perhaps the 5th v 6th debate could possibly have arisen from misreading 5 v 6 on a Gestetner copy of a type written document of the period.
In any event, if you wish to be really pedantic, the aircraft was not known as the Spitfire at the time, but was referred to as the Type 300, the F 7/30(modified) or F 7/30(F 7/34 modified). Supermarine had written to the Ministry on 10th March asking for the name Spitfire to be reserved. The initial reply had been "It has been noted for consideration when, and if, an order is placed for this aircraft." Not until 10th June was Supermarine advised by the Air Ministry that approval for the use of the name Spitfire was given. (Spitfire - The History)
What is the truth? Historians will never be out of work it seems.