Can you tell, based on the SN, what year it was manufactured? I mainly want to know if this particular carbine saw action in the civil war. I suppose it is possible that it was delivered toward the end of the war, but never distributed to the troops.
The problem with the Burnside is the serial # were all over the place. The SRS does not differentiate between the models, so in reality there are 2 Burnside's with serial # 18724. The term 5th model is a collectors term and not really used back then. The 5th model was a 1856 with all the improvements that went into the model 1864. The serial # on the model 1864 were reset to 0 and ran to 19000 so your would have been a late war production. Lets see if we can get @JOHN42768 and @Jeff in Ohio to chime in.
There is not a lot I can add. There were approx. 55500 Burnsides purchased by the Ordinance Dept. in the course of the war. The "5th" is basically a Model 1864 that was introduced in 1863. The 5th was an improved 4th by adding a guide screw in the center right frame that allowed smoother operation of the breech. I would guess it to be very late 1864