We use data collected by the CLEO III detector at the Cornell Electron Storage Ring to measure the inclusive yields of D(s) mesons as B(Y(5S) --> D(s)X) = (44-7 +/- 4.2 +/- 9.9)% and B(Y(4S) --> D(s)X) = (18.1 +/- 0.5 +/- 2.8)%. From these measurements, we make a model dependent estimate of the ratio of B(s)*B(s)* to the total bb quark pair production of (16.0 +/- 2.6 +/- 5.8)% at the Y(5S) energy.