After substituting $x=5$ and $h(5)=11$, you should get an equation of the form $11 = a\sqrt{5-1} + 3$. Think about how to simplify this.

Compute $5-1$ and then its square root. Then move the constant $3$ to the other side so that the term with $a$ is by itself.

Once you have an equation like $8 = 2a$, what operation will isolate $a$? Apply that operation to both sides.

In Desmos, type the expression (11 - 3)/sqrt(5 - 1) into a new line. This comes from rearranging $11 = a\sqrt{5-1} + 3$ to $a = (11-3)/\sqrt{5-1}$.

Look at the numerical value Desmos returns for (11 - 3)/sqrt(5 - 1); that value is the value of $a$ that makes the graph of $h(x)$ pass through $(5,11)$.

The point $(5,11)$ lies on the graph of $h(x)$. That means when $x=5$, the function output $h(5)$ must equal $11$. So substitute $x=5$ and $h(5)=11$ into the function rule $h(x)=a\sqrt{x-1}+3$.

Start with the function:

Substitute $x=5$ and $h(5)=11$:

Now you have an equation with just one variable, $a$.

First simplify inside the square root: $5-1=4$, so $\sqrt{5-1}=\sqrt{4}=2$. Substitute this into the equation:

which is the same as

Now subtract $3$ from both sides to isolate the $2a$ term:

so

From the equation

divide both sides by $2$:

so $a = 4$.