Will USB 3 charge the Galaxy S5 faster than USB 2?

Either your adapter isn't pushing enough power or it's faulty. Either way, you're going to need a new high(er)-output adapter. 2.4amps should be suffice.

This isn't true, if you were to plug your phone into a USB 3.0 port on your laptop with a 3.0 cable, it'll transmit data a lot quicker than it would in a 2.0 or 1.1 port. Not sure if the same rule applies with charging via a laptop, maybe the 3.0 gives it the 0.9 amp, an extra little kick.

Using a 2.0 cable or 3.0 cable for charging with a 2.4 amp mains charger will make no difference at all, they'll both charge as quick if they're both a good quality USB cable.
 
please quit spreading misinformation, USB 3.0 cable are capable of transmittig up to 1.5 amps when there is no data connection and so are ableto charge mmuch faster than USB 2.0 cables. try it for yourself. here's the quickest way:

using the same 2amp wall adapter plugged into the same wall jack connect the USB 2.0 cable to your phone and wait for 5 minutes then check the estimated time until full charge. try again with the USB 3.0 cable instead and you'll find that the estimated time will be less than half.
 
not only that but with USB 3.0 you'll actually see it go up a percent about every 1 and a half minutes compared to barely any change at all on USB 2.0

FYI both cables I used for the test were the original Samsung cables the black 2.0 USB is from my s4 and the white 3.0 was from my s5
 
not only that but with USB 3.0 you'll actually see it go up a percent about every 1 and a half minutes compared to barely any change at all on USB 2.0

FYI both cables I used for the test were the original Samsung cables the black 2.0 USB is from my s4 and the white 3.0 was from my s5

Try the white cable for samsung s5... it is thicker than other samsung white cables. And also thicker than the s4 cable. I compared two oem samsung usb cables, the J5 (thinner cable) and the s5 (thicker)cable, on the same wall charger (S5's 5.3v2A) and yes, they have a difference.

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