Answer
$T$ is a linear transformation from $R^5$ into $R^3$
Work Step by Step
Let $A$ be a $m\times n$ matrix. The function $T$, defined by $T(v)=Av$, is a linear transformation from $R^n$ into $R^m$.
Here, since $A$ is $3\times 5$, implies $n=5,m=3$.
So, $T$ is a linear transformation from $R^5$ into $R^3$