That will work with your headset, it's 1-1/8". Your stem should be fine too (can't see your images at work, but I'm assuming it's a clamp style 1-1/8" stem).
The important part is stack height. If the steerer on the fork is too short you are screwed. It is likely fine, as 5" isn't an extreme steer tube length like some old bikes with threaded headsets had. Measure your existing steerer on the fork (top of the crown to the top of the steerer where it sits inside or above the stem) and as long as you are less than the steerer length for that fork, it should work. I don't expect any problems.
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