If the $x$-intercepts are $r$ and $s$, you can write $g(x)=a(x-r)(x-s)$.

Plug in the point where the graph crosses the $y$-axis (where $x=0$) to determine the value of $a$.

In Desmos, enter each answer choice as a separate equation (for example, type $y=(x+1)(x-5)$, then the other three).

For each curve, check whether it crosses the $x$-axis at $x=-1$ and $x=5$ and whether it crosses the $y$-axis at $(0,-5)$.

Choose the equation whose graph matches the given parabola in intercepts and in whether it opens upward or downward.

The graph crosses the $x$-axis at $x=-1$ and $x=5$.

So the quadratic can be written as

for some constant $a$.

The graph crosses the $y$-axis at $(0,-5)$.

Substitute $x=0$ and $g(0)=-5$ into $g(x)=a(x+1)(x-5)$:

So $a=1$.

With $a=1$, the equation is $g(x)=(x+1)(x-5)$.