Answer
The ordered pair $(2,1)$ is not a solution, but the ordered pair $(5,-1)$ is a solution.
Work Step by Step
We replace $x$ with $2$ and $y$ with $1$ and see if a true statement results.
$y-x \lt -2$
$(1)-(2) \lt -2$
$1-2 \lt -2$
$-1 \lt -2$ False
The ordered pair $(2,1)$ is not a solution since $-1 \lt -2$ is a false statement.
We replace $x$ with $5$ and $y$ with $-1$ and see if a true statement results.
$y-x \lt -2$
$(-1)-(5) \lt -2$
$-1-5 \lt -2$
$-6 \lt -2$ True
The ordered pair $(5,-1)$ is a solution since $-6 \lt -2$ is a true statement.