Melanie,
TF 1145 is the frame number. This frame was used for the SW5 and the DT5 model. With the addition of brakes and a clutch, the DT5 became a SW5. The number is likely too high to be 1928; probably 1930 and later. Many DT5 have been converted into a SW5. One way to tell the difference is how far back the foot rests are. The photos show foot rests in the SW5 location (even ignoring the rear set footrests). On a DT5 the frame lug would be about two inches further forward. Also the DT5 typically only had one footrest, so when the second is added later for road use it is usually just welded to the frame rather than using a brazed lug. The DT5 would also not have a lug for the front brake anchor/pivot. When these are added post-factory, they are often a simple bush punched through the crotch of the girders. The factory used a lug and the pivot that was behind the fork girder. So both suggests this machine left the Works as a SW5 model. Also as time went on and the DT5 was eclipsed by the Rudge Dirt Track and others, sales of Douglas DTs declined, which is why the factory decided to offer the SW5 in 1930-32 and so capitalize on the surplus DT components.
There should not be a number on the head stock.
EL 1326 is a SW5 or DT5 engine. It has a small airbox, which dates from mid-1929 to 1932; essentially a 1930-32 model. This airbox has a oil pump inside; the earlier tall air box did not (hand pump lubrication only). The crankcases from 1928-32 are pretty much the same and interchangeable, but again the number is high enough to suggest 1931-32.
YG 1083 is the gearbox used in the DT5 model. The case was used on a number of different models: OC, TT, DT, and SW5. The prefix code denotes the original gear ratios, and YG was an ultra close ratio for cinder track racing. The correct prefix for a SW5 would be UG (normal road ratios), TG (wide road ratios), or SG (close road ratios). These ratios were also shared with the OC and TT model. The YG ratios are problematic for use on the road as they are actually too close. They are not meant for racing gear changes, rather you selected a ratio for 1/8, 1/4, or 1/2 cinder tracks and you stayed in that gear for the entire race. On the road you are limited in selecting sprockets for a 55mph top gear, or a 20mph first gear; there is not enough spread in the gearbox to have a correct 1st and 3rd.
Of course, that only applies to the original gears that were inside the case. All the gears are interchangeable, so it could have any ratios in it now.
Some pictures of the SW5 gears in this post:
https://www.douglasmotorcycles.net/index.php?topic=1638.msg5896#msg5896A link to a chart on DT/SW (and other) gear ratios:
https://www.douglasmotorcycles.net/aa-files/images/doug/2006/SW-gears/gear_ratios.pdf-Doug
[Fix typos. 19Sep16 -Doug]