Electronic – 2N2222A Mismatch between emitter and collector

Actually I didn't notice this was about an open collector output until miceuz posted his comment, so for OC output I would use one of these

and the isolated version

If the GPIO can't provide enough current to the optodiode to get the appropriate output current in the transistor side then you'll have to add another transistor either to the input or output.

Note that resistor values may vary depending on the requirements

2) How can I figure out what ohm value of resistor to put between the gpio and the base?

A rule of thumb is that you have to provide 1/10 to 1/20 of the output current in the transistor base in order to saturate the transistor and get a low collector-emitter voltage drop (which means higher voltage output and less heat dissipation)

The problem is that your transistor is connected in emitter follower configuration. The output will always be a bit less than the input. The point of a emitter follower is usually current gain, you actually get a small loss in voltage.

It would be better to use a PNP to switch the voltage into the regulator, instead of the NPN you show:

When the digital signal goes high, the emitter of Q2 will be about 700 mV less, or about 4.3 V. That will cause 10 mA to flow thru R1, most of which will be coming thru the collector of Q2, which also means it will be going thru the base of Q1. R2 is only to guarantee Q1 will be off when intended, despite a little leakage and maybe some noise in the system.

You didn't say how much current you need at 5 V, but this needs to be considered. The maximum current Q1 can handle will be its base current times its gain. In this example, the base current is about 10 mA as already shown. With a gain of 30, for example, this setup can support up to 300 mA. If you need more current than that, then changing Q1 to a darlington or a P channel FET will probably be a better tradeoff than increasing the base current.

This circuit is intended to be simple and work with a wide range of parts. Q2 can be just about any small signal NPN transistor. Q1 could be a jellybean PNP if you only need 100 mA or so. Otherwise, a small power transistor may be better.

Added:

You now say that the regulator only needs to supply 30 mA maximum at 5 V. In that case Q1 can be most any jellybean PNP transistor, like a 2N4403. Such small transistors will have more gain than a power transistor. Figure you can count on a gain of 50 minimum, so the base current only needs to be 600 µA. A couple of mA base current would then be enough to put Q1 solidly into saturation. That allows making R1 larger, like 2 kΩ. So here is the final circuit: