For brushless motors too small a prop only means not as much lift. Too large a prop means the motor and ESC overheat, and wastes power and does not fly as long.
I don't have those exact motors. Are they too hot to hold tightly after a normal flight? That is a measure I use to say that props can't be any larger. If they are too hot to even touch, then the props are definitely too big. I have a fixed wing with 2212 kv2000 that I run 6x3.5 on, so I would guess that 5x3 is a little too big for 2204.
Here is an article that discusses props for 2204 kv2300 motors that seems to imply 5x3 is fine:
https://oscarliang.com/best-prop-cobra-2204-motor/With 2 blade props you can easily just cut them down and rebalance if they are too large. You can do this with 3 blade props also. Balancing is only a little more complicated.
If 5x3 two blade is close to correct then I would order some 4x3 three blade and some 4.5x3 three blade if you can find them.
Be aware that the best two blade prop is a little more efficient than the best 3 blade prop.