Once you know $b+1/b$, think about what happens if you square that expression. How can squaring help you create terms like $b^2$ and $1/b^2$?

After you find $b^2+1/b^2$, try multiplying $b+1/b$ by $b^2+1/b^2$. When you expand, which terms combine to form $b^3+1/b^3$?

From the algebra, you can derive or recall that $b^3+\frac{1}{b^3} = (b+\frac{1}{b})^3 - 3\left(b+\frac{1}{b}\right)$. Since $b+1/b = 5$, the value of $f(3)$ equals $(5^3 - 3\cdot 5)$.

In Desmos, type 5^3 - 3*5 and press Enter. The number that appears is the value of $f(3)$; match that value to the correct answer choice.

The function is

so

We are told $f(1)=5$, so

We do not need to solve for $b$ itself; we will work with this equation directly.

Square both sides of $b+\frac{1}{b}=5$:

So

Now we know both $b+\frac{1}{b}$ and $b^2+\frac{1}{b^2}$.

Multiply the two expressions $b+\frac{1}{b}$ and $b^2+\frac{1}{b^2}$:

Expand the left-hand side:

So we have

But we know $b + b^{-1} = 5$, so

which gives

Since $f(3)=b^3 + b^{-3}$, the value of $f(3)$ is $\boxed{110}$.