They explained: "After May 2017, you find you still have some paper £5 notes, you will be able to exchange them at the Bank of England".
After today, shops no longer have to accept the paper £5 note, featuring prison reformer Elizabeth Fry, as payment. It said some other banks and building societies may still accept the old paper £5 notes for a limited period at their own discretion.
The new £5 notes were introduced in September, but there are an estimated 150m of old fivers still in circulation.
The Bank of England said 150 million of its paper £5 notes - the equivalent of about three for every adult in the United Kingdom - remain with the public.
So, if you've got a wad of cash in your purse, wallet or stashed in your piggy bank check to see if you have one or more of the notes that are about to become worthless.
Following the introduction of the new £1 coin in March, the legal tender status of the old "round pounds" will be withdrawn on 15 October.
"However even if it is two or 20 years down the line, the Bank of England will always reimburse people for them".
Instead you will need to use the new polymer fiver with the image of Winston Churchill, which was launched by the Bank of England back in September.
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"The Bank of England will still exchange the old notes after this date - there is no time limit on this".
There are around 150 million paper £5 notes still in circulation and you will not be able to spend them from Saturday onwards.
On Friday the 5th of May, old fivers will cease to be legal tender.
"They don't have a withdrawal date as such similar to the English £5 notes".
The Bank of England website states: "All Bank of England notes retain their face value for all time".
The move to the new polymer £5 note has been controversial.
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.
There are plans to release a new £10 note this summer, which will feature classic British author Jane Austen.