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Released in March 1994, Socket 5 was designed for second-gen P5 Pentium processors among other Intel parts, but could also accept AMD's K5 chips as well as 6x86 Cyrix CPUs and IDT's WinChip series.
The summer of 1995 brought a successor to Socket 5 with the arrival of Socket 7 (Socket 6 was essentially skipped), which likewise supported P5 Pentium processors as well as compatible parts made by AMD, Cyrix/IBM and IDT.
Socket 7 parts are backward compatible with Socket 5 using an adapter (unless you want to modify the pins yourself). The key difference between the two is that 7 has an extra pin for dual split rail voltage versus Socket 5's single voltage.
Super Socket 7 didn't arrive until 1998 and served as a stopgap for AMD, buying the company time to develop its own motherboard infrastructure (Slot A) after losing licensing to Intel's sockets, which had evolved to Slot 1 in 1997.