Synchronizers let you shift gears using the clutch.
The hub is spring loaded so when you move the shifter partway, it presses the baulk ring (internal cone part) against the gear.
When they have slow down to the same speed, the shifter will move all the way in. It happens very quickly, unless the synchros are worn and not working well.
Synchro is basically:
Coupling with hub Baulk rings and gear faces
Coupling with hub. Left: assembled. Right: not assembled
Each synchro set services two gears (arrows). Center arrow points to the Coupling Sleeve
The Coupling Sleeve is what the shifter moves.
FS5C56A 5-speed has very different synchros from other A-series transmissions. It has "C" type synchros (the "C" in FS5C56A) which are very different
4-speed 32604-H1000 RING-BAULK (4) <> 32604-H1010 < 32604-H9000 32609-18000 INSERT-SHIFTING (6) 32603-18000 SPRING-SYNCHRONIZER (4) 32601-18000 HUB-SYNCHRONIZER (2) 32606-18000 SLEEVE-COUPLING (2)
5-SPEED 32601-H7200 HUB-SYNCHRONIZER (2) 32606-H7200 SLEEVE-coupling (2)
Also see 56-Series_Transmission_Parts#Synchros.
B310 with FS5W60L 5-Speed shows this:
Synchro Hub - 1st & Rev Synchro Hub - 2nd & 3rd Synchro Hub - 4th & 5th
For the 4th-5th gear, or 2nd-3rd the coupling is the same part number:
For the Synchro Hub inside the coupling:
32258-H9001 HUB-SYNCHRONIZER 1ST & REVERSE $133.92 USD 32601-H9001 HUB-SYNCHRONIZER 2ND & 3RD 32601-H9000 HUB-SYNCHRONIZER 4TH & 5TH
4-speed and 5-speed synchronizers
FS5W60L 32604-H9000 RING-BAULK 4 32603-18000 RING-SYNCHRONIZER 4 32601-H9001 HUB SYNCHRONIZER-2ND & 3RD 1 32609-18000 INSERT-SHIFTING 6
32602-32200 SPRING-SHIFTING INSERT (SYNCHRONIZER INSERT) 3 * unique to F5W60L 32608-H9000 INSERT-SHIFTING 9 32258-H9001 HUB SYNCHRONIZER-1ST & REVERSE 1