HSBC said it was introducing the notes to a further 210 of its ATMs across England and Wales during the coming two months.
The move follows a trial carried out by the group with the Bank of England in 2009 under which 100 of its cash machines in the South West and Midlands dispensed the notes.
The Bank of England is keen to get more 5 notes into circulation owing to to a general shortage of the notes and the poor quality of those that are used.
There are currently around 1.25bn-worth of 5 notes in circulation in the UK, or 249 million notes, compared with 640 million 10 notes and more than 1.5billion 20 ones.
Because 5 notes get used more regularly than higher denomination notes, they have a much shorter lifespan, with the average 5 note lasting for only one year.
All cash machines can dispense 5 notes but the majority of banks choose to load them with only 10 and 20 ones, as these notes tend to be better quality and using them means the ATM does not need to be restocked as frequently.
But a report from cash machine network Link said that all of the UK's largest banks and building societies that operate ATMs had now put in place plans to start dispensing 5 notes from their cash machines.