These designations were used up until the Blackface Era amps and apply to Tweed, Blonde, and Brown-era Fender amps.
The first number is the decade.
5) Fifties
6) Sixties
The middle letter is the year of the most recent circuit design change or update.
A) 1950
B) 1952
C) 1953
D) 1954
E) 1955
F) 1956
G) 1959
The last number is the amp model, according to this list:
1) Champ
2) Princeton
3) Deluxe
4) Super
5) Pro
6) Bassman
7) Bandmaster

9) Tremolux
10) Harvard
11) Viborlux
12) Concert
13) Vibrasonic
14) Showman
15) Reverb Unit
16) Vibroverb
So a 5F4 would be a 1950's(5) 1956 Circuit update design(F) Super(4).
A 5E7 would be a 1950's(5) 1955 Circuit update design(E) Bandmaster(7).
Corrections welcomed.