See also: The new £5 coin that's set to be worth a fortune
Back in May, for example, auctioneers Spink & Son sold an older fiver for an astonishing £16,800, thanks to its A01 000004 serial number and history - it had been given to then-chancellor Anthony Barber.
Often, old bank notes turn up years or even decades after they've gone out of circulation.
"We all seem to do it; whether it's loose change down the back of the sofa or crumpled bank notes tucked inside an old handbag at the back of the wardrobe, we just can't stop collecting cash," says Rosamund Evans of law firm Barker Evans.
"Over the years, when dealing with deceased clients' estates, I've come across everything from jars full of old pennies and £5 notes big enough to wallpaper a room, to bundles of cash hidden in old soap boxes under a sink."
And, naturally, any notes with errors can be worth more than the face value.
Meanwhile, many of the new polymer £5 notes are also worth a lot more than a fiver.
Most valuable of all is a note containing a tiny engraved portrait of Jane Austen, which has been valued at up to £50,000. Three of the four notes engraved by Graham Short have been found, but there's one still on the loose.
Other notable new fivers include those with very low serial numbers; indeed, one beginning AA01 is currently listed on eBay for £3,900.
And don't forget that you'll soon get another opportunity to try and spot a valuable new note. The new polymer £10 note is due to enter circulation on Thursday September 14 - and, no doubt, low serial numbers will again be in demand.