You need to provide MUCH more information to get any definitive direction or solutions.
As already in the comments you have a Common Anode RGB LED.
Here is the datasheet for an example RGB leaded LED. Notice in this datasheet that both the Blue and Green LED have a minimum Vf of 3.3V so are unlikley to work on a 3.3V I/O pin at all.
Consider the following:
You CANNOT drive this LED directly from an R'Pi. The Blue LED is likely at least 3.4V Vf so will be very dim driven from 3.3V I/O. Green can also have a high Vf and be unsuitable for 3.3V drive.
The LED current becomes a critical factor. The R'Pi I/O should not be used to source or sink high current. It's likely that your LED is at least 20mA per color and it is inadvisable to source or sink this level of current from your MCU.
To control the three colors independently you need THREE PWM pins, one for each color.
To drive this LED you can use the 5V supply, but you CANNOT drive this directly from the I/O pins.
You will need a buffered circuit such as this:
simulate this circuit – Schematic created using CircuitLab
The values of R1,2,3 will depend on the required current for your LEDs and the on resistance of the FETs. You may be able to get away without these resistors if the FET on resistance is high enough (though you'd have to measure these parameters to do this).
You could of course use a very similar circuit based on BJTs, but would need to provide base resistors to limit the base current.
I can't just control every single color with a PWM-signal... why not? \$\endgroup\$