Answer
$252$ different starting lineups.
Work Step by Step
1) It is not a sequence of choices.
2) The order in which the players are selected does not matter.
It is a combination of 10 distinct players taken 5 at a time:
$_{10}C_5=\frac{10!}{5!(10-5)!}=\frac{10!}{5!\times5!}=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times5\times4\times3\times2\times1}=252$
