DC and AC analysis of a Common Emitter Amplifier Circuit
Vout is on the collector. That 0.7v figure you have in your head is for the base-emitter drop. 

If you want 10v out, and 5v VCE, then the emitter will be at 5v, and the base at 5.7v. With Re and Rc drops of 5v and 10v respectively, then at 2mA you can calculate their values as 5/2m = 2.5k and 10/2m = 5k respectively.

You mention Ibmax, but you don't give any figure for beta. 100 minimum is a reasonable value. So if you set the base bias chain current at Ic/10 = 200uA, then 5.7/200u = 28.5k for R2, and 14.3/200u = 71.5k for R1. 

The actual bias point will be slightly different to the voltages assumed, due to ignoring base current. However, the point of this sort of bias arrangement with a large Re is that it's very tolerant to transistor variations.