After effects loop part of movie clip
LoopOut() loops after the last keyframe, and by default it loops all the keyframes. Unless you have a specific need to use expressions, this would be easier to achieve by just setting keyframes. 


Once you have time remapping enabled, go to the 3 minute mark and add a keyframe. 
Then go to the frame one frame before 4 minute mark and add another. 
Select the last three keyframes (3 minutes, 4 minutes and 5 minutes in your example). 
Copy them ctrlc. 
Delete the last keyframe
Park the playhead one frame after the 4 minute keyframe and paste ctrlv. The 3 minute keyframe should be at the exact 4 minute mark. Since the timing of the subsequent keyframes is undisturbed, the video will run at the right speed.


Your keyframes should look like this:

0=====3+++④3+++④=====5 ←keyframes 
0.....3....4....5....6 ←time


(the ④ indicates the frame one frame before the four minute mark)


for extra credit change the first 4 minute keyframe (the one that has the 3 minute keyframe right after it) to a hold keyframe (Right-click and Toggle Hold Keyframe). This is because if you have motion blur or frame blending on it can cause strangeness as the layer is "rewound" between the two keyframes.