You would subtract the Vf of the LED from 5V and use that to calculate Rc.
With respect to Rb most people just grab a 1K to 4.7K resistor and call it good. You always want a few times more current reaching the base just to make sure the transistor is saturated so calculating the value with the precision you have done is a bit overkill.
And again with my earlier suggestion you're still thinking 100ma of current. You only need about 5ma. In my project I sent the beam 3 meters with a TSALxxxx LED (don't recall which one, but it was a 100ma max like yours) and only needed 10ma of current.