According to the Long Branch documents by T.H.Marshall, the Production Manager who wrote up the factory report upon closing in 1946, Long Branch had done all the engineering for the No.5 expecting a post war order. More than likely they made a few prototypes. However, they never received an order, and closed the operation in August 1945 with no No.5's produced.
Here's what Marshall said in his report:
1945 - 1st Quarter:
During the first quarter of 1945, instructions were received to proceed with the engineering, planning, and tool change necessary to produce the No.5 Rifle at a rate of 8,000 per month. No orders were received for actual production, but the engineering work pertaining to planning the conversion was in hand. Production of this rifle was not considered a major project, as most of the components in the No.5 rifle are common to the No.4 Rifle.
2nd Quarter:
Engineering, planning, tool procurement and tool proving were temporarily suspended on the No.5 Rifle to allow speedy processing of an order received for Mauser firing pin and extractor components. The company was advised that the No.5 Rifle(BritishLightened Pattern) would not be considered for production in Canada
at this time. Consequently, no further action was planned for this project by the company. All tooling and ‘tool proving billets’ were placed in stores and recorded.