i find it easiest to work "backwards".
You know you want to control 5V @ 56mA.
So you need a transistor with at least V
CEO of 5V. The BC550 is good up to 45V, so that is fine.
And the transistor needs to be able to control at least 56mA. BC550 is rated ("I
C") for 100mA. You probably wouldn't want to use a transistor with any less than 100mA rating.
Your BC550 has a "worst case" (minimum) current gain of 110x.
And we would like to drive the transistor into AT LEAST 2x "saturation"
So, doing the calculation in my math-deficient brain, if I drive a 100x transistor with 2mA of base drive current, it will cause it to have a maximum of 200mA of collector current. Of course we know it will never actually reach this current because we know what the load voltage and current is from our previous design steps.
So, Ohm's Law says that if we have a 3.3V drive voltage (from an Arduino, perhaps?) and we want 2mA of current into the base of the transistor, we need around a 1.6K ohm resistor. I use my Ohm's Law online calcuator here:
http://www.rcrowley.com/eirp.htm). Actually I would use a much lower resistance value more like 1K or even lower just to remove any shadow of doubt that we are driving the transistor into saturation.