To write an equation for the function that follows these transformations, we'll start with the base function:

$y = \sqrt{x}$

Now, let's apply the specified transformations:

1. Reflection across the y-axis: To reflect a function across the y-axis, we replace $x$ with $-x$. This gives: $y = \sqrt{-x}$

2. Shift 8 units to the right: To shift the graph to the right by 8 units, we replace $x$ with $x - 8$. Applying this to the current function: $y = \sqrt{-(x - 8)}$ Simplifying this: $y = \sqrt{8 - x}$

3. Shift 5 units up: To shift the graph up by 5 units, we add 5 to the function: $y = \sqrt{8 - x} + 5$

Thus, the final equation for the function is: $y = \sqrt{8 - x} + 5$

Would you like any further details or clarifications on this? Here are 5 questions to explore further:

1. How do you reflect a function across the x-axis?
2. What happens if you shift a function left instead of right?
3. What if you combined vertical and horizontal stretches with these transformations?
4. How would this function change if you reflected it across the x-axis instead?
5. How can you identify these transformations visually on a graph?

Tip: When reflecting a function across the y-axis, always replace $x$ with $-x$ inside the function.