2N2222 base resistor

I think its worth an extra safety factor to ensure the transistor is driven into full saturation - make the base current say twice the calculated value for worst-case hfe...

If a transistor is still on the borderline of linear region and saturation it's Vce could be higher and less predictable. A factor of two or so will probably cover the obscure effects you haven't allowed for like logic high drooping under load, lower than nominal 5V supply, hfe depending on Vce, or whatever.