Did you check the small print on the chargers? If the old one or a generic one was not rated for 2.1A (2100 mA) it would charge slower. The data cable also has to be rated to carry 2.1A to transfer that current from the charger to the device.
The data leads (wires) have nothing to do with charging, only data transfer (2 separate wires for data & 2 for charging in the cables) So a USB 2.0 cable rated to carry 2.1A would charge the S5 just as fast as a USB 3.0 as long as both are rated to carry 2.1A. Same with the chargers as long as both produce 2.1A. Data cable length can also play a small part...