Replace 5-pin push button in my laptop
The switch is probably a SPST-NO tact switch with an earth connection to the metal top (for ESD protection reasons). The earth connection would be the center connection on the right. 

If you want to simulate the switch closure you can short either of the two left to either of the two right (top/bottom) connections via a switch. There is no necessity to remove the existing switch unless it is shorted (unlikely). Here is a datasheet from a similar product. 

Schematic (in the same orientation as your photo):