Yep, that is probably the serial number.
And I would say that one that is 5xxx was probably made back in the early 70's.
Someone could have replaced the brass trigger guard with either the guard off of a Renegade if it is the T/C Hawken design, or maybe one of the Hawken Shop parts to "Hawkenize" the T/C Hawken. You can always replace the wedge plates with Renegade ones and use Brass Black to color the nose cap, the patch box and the butt plate. Or, I think the Hawken Shop has steel replacement parts for most all the hardware on your rifle.
And if it is a .50 caliber, as most of the older ones were, that can be cured by having the barrel drilled out to .54.
Regardless of what you do, those old T/C's were rugged guns. If the mainspring plunger has the wasp waist end on it, I would replace that with the newer model. Those old ones were known to break from time to time. Else, problem free.
Enjoy. A photo or two would be a good thing to post also.
John (Bigsmoke)