It looks like a transition badge snare to me. But just take the heads off and measure instead of guessing. Not many out there, though I have had one or two over the years.

Rogers Dynasonic, 1975, first generation Big R Transition. I cant see your number but it looks like its in the mid 14K range. Oval badge era Dynasonics had their own badge number sequence. Big R era Rogers Drums used the same badge numbering for all drums, snares and drums of all kind. Over the past three years I have devoted quite a bit of time to observing drums for sale on ebay and have noticed quite a few things for big R drums. One of them is that serial numbers are much more reliable than previously supposed. Another is that there were two seperate transition periods for Big R Dynasonic snare drums. Yours is in the first transition period. The second transition period begins with serial numbers in the high 14K range through the mid 40K range. On those drums, the Big R badge is in the NEW location, two panels to the left of the throw off, and there is no dampener. All of these drums, first gen and second gen transition pieces, have five digit serial numbers. These drums date from 1975 into early 1976. There is some overlap in shell use, because I have seen a first gen transition snare drum with a number in the 22K range. However, based on observations, first gen snare drums above 15K are less prevalent than the second gen snare drums. so there are fewer and fewer of them as Oval Badge Shell stock ran out.

Your drum is a five incher.

WOW!! It's nice to know so much about this drum! And there is a dampener for it, but I actually removed it because I never used it. This drum is claimed to be 1977, so is it possible the shell was made in '75-'76 and the drum itself was finished in '77?

Anything is possible. But this drum is 1975. five digit number. 1975 all day long. It might not have been sold till late 76/77.