Wikipedia says they were 5¼". But then it says "citation needed" so that may not be reliable.
Jay Helfert has written about this several times.
From 2011: "I was in that poolroom a couple of times in the 60's and even played on the same table. It was a typical over-sized 4x8 that was popular in Midwestern poolrooms back then. Not the toughest table in the world, but not the easiest either. Those old boxes had straight cut pockets with fairly deep shelves. I'm guessing the pocket openings were just under 5". You had to hit the pockets though or the ball wasn't going in. Shooting down the rail was probably easier than most tourney tables in use today, but out on the table you had to make a clean shot."
From 2009: "It was what we called an "over sized" eight footer (46"x92" playing surface). It just seemed like a normal table to me back then. What did I know? Based on the Sport Kings that were so popular in Midwestern poolrooms at that time, I would guess the pocket openings at about 4.75". But remember the slate was fairly deep on those old tables and the pocket opening were straight cut with very stiff rails."
From 2007: "I visited East High Billiards in the 60's when my friend Russ Maddox owned it. The 4x8 tables they had there were the over sized Sport Kings (46" by 92" playing surface) with approx. four and five/eighths inch pockets. These were very popular tables in Midwestern poolrooms in that era. ... I played on these tables quite a bit growing up, and they were great pool tables. The pockets were straight cut and "stiff", and you had to hit them cleanly or the ball would not drop. The slates were not shallow either. George Rood played in that same club quite a bit and was a terrific 14.1 player. I doubt he ever ran over 200 balls there. He and Russ were friends and George often remarked that he thought Mosconi's run of 526 was amazing."