I've picked up another 8"-by-10" Yankees Action picture pack. I believe it is from 1956. My opinion are the years I have are 1953, 1955, 1956, 1957, and 1960. I think the checklists for the various years may be as listed below. Even though I don't have the 1958 or 1959 sets, I based the checklists on the sets Mike and Steven have. I've also attached photos for the sets and envelopes they came in. Unfortunately, for some reason, the pictures for 1955 and 1960 are not being uploaded, something about a security token being missing. The following checklist is purely speculative on my part. It may be that more than one distinct set was issued during a year. It is also possible that a set was issued for more than one year. Also, sorry for the large envelope pictures. I have jpegs of them in a smaller size with the player photos, but none of them would load because of a missing security token.
Yankees Action Photograph sets.jpg
1953
Year based on inclusion of Whitey Ford who returned from the service in 1953 and Johnny Mize and Vic Raschi who last played for the Yankees in 1953..
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1953 Envelope.jpg
1955
Based on Elston Howard and Bob Turley first playing for the Yankees in 1955.
1955 Action Envelope.jpg
1956
The only differences between this set and the previous set is that Grim is out and Martin is in. It seems either set could be 1955 or 1956. The envelope is interesting in that it indicates the set came from Manny's.
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1956 Action envelope front.jpg 1956 Action envelope reverse.jpg
1957
The only difference between this set and the previous set is that Rizzuto is out (he retired after the 1956 season) and Larsen is in (he was the hero of the 1956 World Series).
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1957 Action envelope.jpg
1958
The only differences between this set and the previous set is that Collins is out (he was not on the team after 1957), Martin is out (he was traded during the 1956 season), Tony Kubek is in (he first came up in 1957) and the multiple coaches/Stengel is in. Dickey stopped coaching for the Yankees and became a scout after the 1957 season, so it is possible this is from 1957 instead.
1959
The only difference between this set and the previous set is that the multiple coaches/Stengel is out and the lone Stengel is in. Dickey stopped coaching for the Yankees in 1957 so it makes sense to replace with just Stengel.
1960
The differences between this and the previous set are that Bauer is out (left Yankees after 1959 season), Carey is out (not sure why), Larsen is out (not with team after 1959), McDougald is out (not sure why), Ditmar is in, Lopez is in, Maris is in, and Richardson is in.
1960 Action envelope.jpg