The Tempest Mk V prototype flew for the first time on 2 September 1942, with P.G. Lucas at the controls. Flight trials highlighted the need to restore lateral stability lost because of the extended nose and the prototype was modified with a fin fillet and increased span horizontal stabilizers.
It was realized that, although the Tempest V´s performance was less spectacular than anticipated from the other prototypes with there more advanced engines, all of these other aircraft would take far longer to develop to a point where they would be ready for production. A decision was made to concentrate Hawker´s efforts on the Sabre II powered aircraft in order to get the new fighter into operational service as soon as possible. In 1942 400 Tempests were ordered before the prototype´s first flight (originally Mk Is).

 Tempest Mk V were built in two variants, Series 1 and 2. These are the differences:

          Tempest Mk V Series 1:

• The Series 1 had its Hispano Mk. II cannon protruding ahead of the wings leading edge.
• The joint between the rear fuselage and tail unit was reinforced as a measure, by riveting over with fish plates thus rendering the tail unit nondetachable.
• The rear spar pick-up end fitting was cranked in order to pick up the fuselage lugs. This was because the fuselage structure of these early aircraft were converted Typhoon assemblies, whose rear spar pick up lugs were too high to allow direct attachment. The top wing root fillet fairing had to have a bulge in it to clear this fitting.

          Tempest Mk V Series II:

• The Mk V Series 2 were fitted with the new short-barrelled Hispano Mk. V cannon which was completely enclosed.
• The built-up tubular steel fuselage rear spar pick-up structure was replaced by a one-piece casting which gave a direct pick up making a much simpler structural joint.
• The reinforcement of the rear fuselage was not necessary allowing a detachable tail unit.
• Provision to carry two 45-gal drop tanks.

 The first 100 aircrafts (Series 1 with serialnumbers in the JN range) were manufactured at Langley in Buckinghamshire. The first production aircraft (JN729) made its maiden flight on June 21 1943. 
The other 300 Mk Vs were built at the Gloster company and were Series 2 with EJ serialnumbers. Two further orders were placed, all Series 2 standard with NV and SN serialnumbers.

Sources:
Hawker Tempest (4+ Publication)
Typhoon/Tempest in action (Squadron/Signal Publications No 102)
The Typhoon & Tempest Story (Chris Thomas & Christopher Shores)
Scale Models February 1973, by Bob Jones