Shops can stop taking them after they cease to be legal tender on Friday night, but banks should still accept them all weekend.
So people are being encouraged to check their belongings and houses thoroughly or take the risk of of being stuck with worthless notes.
A public consultation has been launched by the Bank into how it produces new £20 polymer notes.
"It is important for consumers, retailers and other businesses to be aware that on 5 May 2017, the older paper Bank of England £5 notes featuring Elizabeth Fry will be withdrawn from circulation".
They are to be withdrawn from circulation and by Saturday, May 6 only the polymer note will be accepted.
The change to polymer £5 notes marks a temporary absence of women, apart from the Queen, on the Bank's banknotes.
But there are an estimated 165 million old fivers still in circulation.
Banks will continue to accept or replace any old £5 notes brought into a branch by their own customers.
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If you have an old £5 note that you've been meaning to spend you better get your act together because tomorrow is your last chance.
What should I do if I still have old fivers in my purse/wallet?
"All Bank of England notes retain their face value for all time".
Generally, you will need to be a customer of the bank or building society to make a swap.
What can you do if you discover an unspent old note after May 5? If you are doing it by post, there is a form to fill in first.
But there's no time limit on swapping them with the Bank of England.
The Bank of England had hoped the new plastic note would be much harder to fake than the old version, due to the extra holograms and the see-through panel.
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".