Formula not recognizing deposit amount from Pop Up Menu

Not really your fault. It is a quirk of pop up menus and, in your formula, comparing actual numbers to text. In your formula you need to ask if H5=50, not if H5="$50.00". Same with the other numbers. Or you can leave your formula alone and create your pop up a different way so all items are text.

When you use the sidebar to enter each item one at a time into the pop up, Numbers tries to figure out what the data format should be for each separate item. In your case the first item "Not Required" gets formatted as text while the $50.00 and other numbers get formatted as currency, not text. You might have noticed when entering the numbers that if you typed $50 it got turned into $50.00 whether you liked it or not. The $50.00 in the pop up is 50 (the actual number 50) formatted as US currency, it is not the text "$50.00". When your formula checks if H5="$50.00", it does not.

You probably want the numbers in the pop up to be actual numbers (which they are), not text. As actual numbers, you can use numerical formulas such as SUM to sum the column of deposits. If they were all text, SUM would be zero because it ignores all text, even text that looks like numbers or currency.

Here is an easier way to make a pop up menu that also lets you specify the data formats if you want to:

1. Enter your items in a column of a table, one item per row. Usually you would do this in a separate table on another sheet. You can format the entire column as text (usually before entering any items) or keep them as "automatic" or format each item however you want. I recommend not formatting numbers and dates and such as text unless every item in the pop up is text.
2. Select the column of items and format them all at once as Pop Up Menu. This will turn them all into pop ups that have all the items.
3. If you included a blank cell as an item, the pop up menu will "start with blank". If not, you can choose to have it "start with blank" if you want it to.
4. Copy one of those pop up menus and Paste it where you need it.
5. To edit the pop up later, select all the cells and format back as automatic (or as text if your pop up has numbers or dates formatted as text) to revert them from being pop ups. Edit them. Add or delete items. Go through the steps above to turn it all back into a pop up. Copy/Paste the new pop up where you need it.

BadUnit nailed it with the display formatting being the issue - Numbers sees the cell value as the number 50 (or 100, etc.), even though it displays as $50, $100, etc.

As an alternative to the IFS() statement, you could use SWITCH() which is an easier approach to selecting an answer from a fixed list:

SWITCH(H5,
    50,"Basic",
    100,"Standard",
    200,"Intermediate",
    300,"Complex",
    "Not Required"
)

This checks the value in H5 agains a list of possible value/result pairs, the first match returns the corresponding result. No match returns the default value "Not Required".