We start with the base function:

$y = \sqrt{x}$

Now, let's apply the transformations step by step:

1. Reflect about the x-axis:

To reflect the graph about the x-axis, we multiply the entire function by $-1$. The function becomes:

$y = -\sqrt{x}$

2. Shift up 3 units:

To shift the graph up by 3 units, we add 3 to the entire function. The function now becomes:

$y = -\sqrt{x} + 3$

3. Shift right 5 units:

To shift the graph to the right by 5 units, we replace $x$ with $(x - 5)$. The final function is:

$y = -\sqrt{x - 5} + 3$

Thus, the function that is finally graphed is:

$y = -\sqrt{x - 5} + 3$

Do you need more details or have any questions?

Here are some related questions you might find interesting:

1. What would the function look like if it were shifted left 5 units instead of right?
2. How would the function change if reflected over the y-axis instead of the x-axis?
3. How does shifting the graph down by 3 units affect the equation?
4. What would the graph look like if no reflection was applied, but the shifts remained the same?
5. How do transformations like stretches or compressions affect square root functions?

Tip: Always apply horizontal transformations (shifts left/right) before vertical ones when solving transformation problems.