Riddle Me This: Boxes of Cash!

Test your skills of deduction with the June 2023 edition of Riddle Me This: Boxes of Cash!

There are three closed boxes on a table. Each box contains $5, $10, and $20 respectively, in five-dollar bills. The $10 box contains two five-dollar bills; the $5 box contains one five-dollar bill; and the $20 box contains four five-dollar bills.

However, they are labeled incorrectly. Someone has taken out three five-dollar bills from Box A.

Can we now determine the correct labels and real contents of the boxes?