Use some nice big NMOS transistors, and the slowest PWM you can bear. Might need to drive the gates higher than 5V to avoid heating.
As those LEDs have only 4 connections, they are either common anode or common cathode. You need to determine which. The connection on the left is probably the common one. To determine the polarity, connect your power supply between that connection and one of the others through a 10K series resistor and see if there is a faint glow from it. If necessary, do it is a dim light and reduce the resistor to 1K.I suggest you drive them through a mosfet+BJT constant current circuit, because your power supply gives very little spare voltage so a series resistor won't give good current regulation. The details of the mosfet+BJT circuit depend on whether the led is common anode or common cathode.