It's really difficult to limit it to five. Among those that deserve mention:
Colt Patterson: First practical revolver
S&W Model 1: First handgun to use self-contained metallic cartridges
Colt SAA: Influence for just about every single-action revolver design after it
S&W Model 3 Russian: First handgun to use inside-lubricated bullets
Colt M1892 Army & Navy: First successful swing-out cylinder DA revolver
S&W Hand Ejector: Basis for the most successful line of revolvers in history which also spawned several milestones such as Magnum handgun cartridges and stainless steel handguns.
Borchardt C93: First semi-automatic handgun
Mauser C96: First successful semi-automatic handgun
Colt 1911: First successful tilting-barrel semi-automatic
Walther PP/PPK series: First successful DA semi-automatic
Browning GP-35 Hi Power: First successful high-capacity semi-automatic
S&W M39: First semi-automatic to be adopted by a major U.S. police agency
Colt Patterson: First practical revolver
S&W Model 1: First handgun to use self-contained metallic cartridges
Colt SAA: Influence for just about every single-action revolver design after it
S&W Model 3 Russian: First handgun to use inside-lubricated bullets
Colt M1892 Army & Navy: First successful swing-out cylinder DA revolver
S&W Hand Ejector: Basis for the most successful line of revolvers in history which also spawned several milestones such as Magnum handgun cartridges and stainless steel handguns.
Borchardt C93: First semi-automatic handgun
Mauser C96: First successful semi-automatic handgun
Colt 1911: First successful tilting-barrel semi-automatic
Walther PP/PPK series: First successful DA semi-automatic
Browning GP-35 Hi Power: First successful high-capacity semi-automatic
S&W M39: First semi-automatic to be adopted by a major U.S. police agency