People have until the end of the day on Friday to spend old paper £5 Bank of England notes in shops before they lose their legal tender status.
May 5 marks the last day that the banknote featuring prison reformer Elizabeth Fry will be legal tender. Around 150 million of the notes are still in circulation.
After this date, shops no longer have to accept them as payment.
The Bank said some banks and building societies may continue to accept the old fiver after May 5 - but this is at their own discretion so people may want to check their bank or building society's policy.
Several major banks and building societies have said that customers can continue to deposit old fivers after May 5.
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 Post Office said its branches will accept the notes as a deposit into any main UK bank account after the May 5 deadline.
Martin Kearsley, banking director, Post Office, said "We offer free cash withdrawal and deposit services for customers of all main UK banks ...
"We'd like to reassure people that there's no end date to depositing paper £5 notes into bank accounts at local Post Office branches, we will still accept them after the 5th of May deadline."
The Bank of England will continue to exchange the old £5 notes for all time, as it would for any other Bank note which no longer has legal tender status.
Old paper fivers and the new £5 note have co-existed since the polymer banknote was first issued by the Bank in September 2016.
The new Bank of England fiver is stronger than its predecessor and boasts new security features making it harder to counterfeit.
But it has been controversial as it emerged that traces of animal-derived additives were used in its production.
A public consultation has been launched by the Bank into how it produces new £20 polymer notes.
The Bank previously said it has held off signing supply contracts for the £20 polymer note, which is due to be released in 2020, in order to better understand "the range of public opinion" surrounding the use of tallow in banknote production and explore potential plant-based substitutes such as palm and coconut oil.
In September this year, the Bank will issue a new £10 polymer note featuring author Jane Austen, recognising "her universal appeal and enduring contribution to English literature".
A spokesman for the Committee of Scottish Clearing Bankers, which represents Bank of Scotland, Clydesdale Bank and Royal Bank of Scotland, said previously: "The paper Scottish fivers are not being withdrawn from circulation, they are just not being reissued.
"They don't have a withdrawal date as such similar to the English £5 notes."