You can try this trick on the calculator, but it will also work with a pen and paper. (With this calculator, you have to hit the equal (=) sign after each operation.)
Enter the number of the month of the birthday
Multiply that number by 5
Add 6
Multiply by 4
Add 9
Multiply by 5
Add the number of the day of the birthday
Subtract 165
The result will show the first one or two numbers as the month and the last two numbers is the day of their birthday.