Step 1 :The question is asking to construct a graph for the function \(y=x^{2}-3 x+5\) within the range \(-3 \leq x \leq 2\).
Step 2 :Generate a range of x values within the specified range and then calculate the corresponding y values using the function.
Step 3 :Plot these values on a graph. The graph shows the shape of the function within the specified range.
Step 4 :\(\boxed{\text{The graph of the function } y=x^{2}-3 x+5 \text{ within the range } -3 \leq x \leq 2 \text{ is as plotted.}}\)