but there are two 5 V pins on the board so which one should I solder?
These two pins are connected, when you look on the copper on the PCB.
So the answer is: to both, someone decided that a single contact hadn't a sufficient capacity.
p/s: does my monitor power require 5V or 12V?
Certainly looks like it has contacts for both, so both Why would you think it only needs either when it clearly has a supply that supplies both?
I planned to use the SATA to 5 V cable to power the LCD control panel board
Make very sure your actual video source has the same understanding of "ground" as your SATA ground. Otherwise, you're risking high ground currents. (The supply for the screen was possibly isolated, so that this never becomes an issue)