State in which of the following quadrants the point $(5^{-3},5^{-2})$ lies.

Let the given point be $(x,y)=(5^{-3},5^{-2})$.
Evaluating the coordinates:

$$x=5^{-3}=\frac{1}{5^3}=\frac{1}{125}$$

$$y=5^{-2}=\frac{1}{5^2}=\frac{1}{25}$$

Since both $x>0$ and $y>0$, the point has positive coordinates along both axes, meaning it lies in the first quadrant.