(slang)(euphemism)
1. the act of shoplifting, petty theft.
2. taking an object, using all five fingers, and concealing said object within an article of clothing or a bag.
3. occasionally a coupon can be used along side the five fingers
The punishment for thievery in certain middle eastern countries possibly includes cutting off all five fingers from the hand that stole the goods. Hence, your discounted price of $0 includes five of your fingers, or a "five finger discount".