Does the sim card in a galaxy s3 fit a iphone 5?

Does the micro sim card fit the iphone 5

Yes.

No
The SGS III micro sim card, the IP5 nano sim card.

The question is why did you DOWNGRADE?
Everyone recommends the IP5 and NEVER mentions the price?

IPHONE prices / tariffs on any all networks defy logic and gravity
Slick advertising does NOT mention this which "Business Insider" has Identified,

The Samsung Galaxy S II was released in MAY 2011 & has 1.2Ghz Dual Core processor with an 8Mp camera, 18 months later November 2012 Apple puts a 1.2Ghz Dual Core processor & 8Mp camera in a phone and call it the IP5

So in addition to the 8 you lose BLUETOOTH MEDIA TRANSFER by moving from the SGS III to the IP5