You're welcome at surplusrifle any time mate. There were only two factories that manufactured the No5 Mk1 ... Fazakerley being the most common and BSA Shirley. If it isn't one then by process of elimination, it must be the other. The correct sights for the No5 Mk1 are the No5 Mk1 singer type sights, you may know it as a Ladder sight ... the difference is the No5 Mk1 ladder sight is marked to 800 yards as opposed to the 1300 yards of the No4 equivalent. The 300/600 flip battle sight is only for the No4 rifles and generally these were produced for the Mk1* models ... though years in civvy street has resulted in all the sights being swapped around on different rifles.
The No5 sling was a jungle green web sling, typical of the British canvas style, though you'll be fine with the standard khaki version also.