The Burnside-built Spencers were indeed .56-.50 Spencer rimfire. Lest the cartridge nomenclature confuse you, the numbers refer to the nominal outside diameter of the case just ahead of the rim and at the case mouth. Actually, the correct nomenclature is Spencer Repeating Rifle (Carbine), cal. .50. The bullet diameters varied from .515 to .520" depending on the manufacturer of the ammo. The advantage of the new cartridge design was/is that the bullet lubrication is inside the case, whereas the .56-56 round used in the M1860 Spencers were outside-lubed "heel" bullets with the bullet diameter outside the case about the same as the case itself at the mouth of the case.
Don't get discouraged by the fact that the M1865 Spencers missed the Civil War. A number of the cavalry units were armed with either. Some companies of the 7th Cav, for instance, were armed with the M1860 and some with the M1865! Imagine the logistics problems that created! In point of fact, you can load a .56-50 round in a M1860 and with softer bullets and black powder, the bullet might "slug up" to fill the larger bore, though more probably the bullet might rattle down the barrel. (Spencers were not regarded for their accuracy, but I'd bet that rep was due to using the smaller diameter ammo in the larger bore!
) While it is true that Spencers were eventually surplussed off, I'd bet this one saw action in the Indian Wars campaigns.