I'm also debating on whether or not I should make sets of change gears for these as I see they're hard to come by for the #5.
The problem with No. 5 change gears is that they're diametral pitch 14 - which is a size which was not that common back then - and possibly never produced by Boston Gear (who kind of set the market direction in these sort of thing.)
However, it is possible to use a complete set of something else. The Barnes 4-1/2 is DP16 and these are quite common from various sources including Boston Gear - although that latter is not necessarily recommended as you can buy three DP16 gears on ebay for the price of one from Boston Gear.
That is if you have NO gears.
Also, and this is relatively new, there are advertisers on Ebay who are marketing plastic jet "printed" change gears, and doubtless they could produce anything you might need.
Speaking of gears, do you have the large "104" gear? I haven't examined your pictures closely. (Edit:I see now you have the 104!) If you have this it might lead you more certainly at keeping it DP14. This large gear is used for most "normal" turning on the Barnes 5 as it yields a much finer feed than the other TPI aimed gear.
Be careful moving that lathe when standing on a concrete floor by "pushing" it while standing on the legs. Two bolts hold the legs, and the bolts are not necessarily made to current standards of strength. A leg bolt that breaks causes the end of the lathe to drop, hit the floor, and the 104 gear invariably gets trashed in the impact - so be careful out there. Resist a natural tendency to slide the lathe: rather lift or pull gently.
Yours is a true treadle lathe. The treadle version was available for a large part of the production years for Barnes Lathes, but the velocipede was MUCH more popular and more widely sold. This one might be worth keeping treadle simply because it is treadle. As such it transitions into the "rare of the rare."
The details of the treadle parts I can't really help you with, (velocipede on both of mine) but someone here doubtless has the treadle version and will be able to help.
Good luck!
Joe in NH