From Saturday onwards, shops may refuse the old note featuring Elizabeth Fry, but banks can exchange them.
So, if your bank, building society or Post Office is not willing to swap your old fivers you can swap them with the Bank of England either by sending them through the post (at your own risk) or visiting its London HQ in person.
SCOTTISH banks' paper £5 notes are not being withdrawn from circulation - as preparations are made to phase out their Bank of England equivalents.
A public consultation has been launched by the Bank into how it produces new £20 polymer notes.
Reports of the death of banknotes may be greatly exaggerated, according to the Bank of England.
The paper £5 has been replaced by the polymer note featuring Sir Winston Churchill.
Friday 5 May is when paper £5 notes officially cease to be legal tender, and the plastic fiver takeover is complete.
If you've got any of the old five pound notes left, today is the day to spend them.
Note that old Scottish £5 paper notes are still legal tender and will be gradually replaced by the new polymer versions.
The Bank of England says it regularly reviews and updates its notes to take advantage of advances in banknote design and security.
What happens to the £5 notes when they are withdrawn?
Barclays - Barclays customers can continue to deposit the paper £5 note into their business or personal account.
But some said it was a good idea for people to give themselves time to hand in old fivers rather than leaving it until after they have lost their legal tender status.
The Bank recently said it would not redesign and reprint those in circulation, but it was still working with its polymer supplier to "determine what alternatives might be available" for the current £5 note and the Jane Austen £10 polymer note.
If you're sending £1,000 or more, you'll also need to include a copy of your ID and proof of address.