Yes, MR16 bulbs do need a transformer. This is because LED MR16 bulbs do not run on standard line voltage. Most MR16 bulbs need a transformer from line voltage to 12V AC/DC. The transformers must be either magnetic (L type) or electronic (C type) to power the lamp.
The main difference between GU5.3 and GU10 bulbs is the spacing between the pins. The GU10 has 10mm spacing while the GU5.3 has 5.3 mm spacing. Another difference is that the Gu5.3 uses a push in method for its prongs while the GU10 uses a twist and lock method to install. A GU5.3 needs a 12V transformer to function. A GU10 on the other hand, runs on 240V which happens to be the same as a home’s electricity meaning you will not need a transformer.