Switching relay with NPN BJT
Am I missing anything?  


YES 


hFE drops to &lt;10% when Vce(sat) &lt;1V at max current, 


but you only need 50mA out, so base current (ideal°) is 10% or 5mA
The load V/R determines the Ic value, not hFE 
but Ib can limit Ic as well if Vce is not saturated




  ° Note: ideal meaning guaranteed specs for Vce(sat)  , although if you know margins and operating temp range, Ideal may be most efficient Ib that does not compromise Relay speed vs Vout for arc suppression and MTBF (advanced design principles)


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  Does this all look good?? 


NO Completely missing understanding of BJT as a saturated switch


examine all these graphs below then in future search/Look for another OEM semi datasheet that shows graphs  (typ only)until you realize hFE=\$\beta \$ or Ic:Ib=10 is de facto standard for reliable switching, not the linear range used for Vce>1~2V(min)
ONSemi is better in this case, But everyone agrees in tables for hFE=10 when Vce= Vce(sat) for worst case specs. These are "gold" standards for interchangeability.
Using hFE= 10 is a conservative "de facto' stanadard for high power but you can often get away with hFe=30 (maybe 50) over temp if you can tolerate higher Vce. (Ic*Vce(sat)=Pd)
Diodes Inc and TI do make special ultralow Vce(sat) ultra high hFe BJT's with very low ESR or rCE values in milliohms but $$$


So if you look at graphs below and locate Ib= 5 mA for a load of 50mA, what is real Vce(sat) @25'C then recalculate coil current and compare with worst case needed. ( it should be &lt; 50mA ) in order to estimate design margin and relative speed of contact switching.

note relay current gain at max contact rating is better than a transistor but slower.  Icontact=16A (resistive) Icoil=50mA therefore current gain of relay= 16A/50mA =320  ( Power gain is even more)







simulate this circuit &ndash; Schematic created using CircuitLab







simulate this circuit
Relay spec for 5V is 100 Ω


  Thus Rb from 3.3 to Vbe = 50 %V drop/Vload reduces 1000 Ω to 500  Ω