As has been stated here; the £5,000 nil rate band is available to everyone.
I think your confusion lies towards the contribution of the income tax calculation.
The £5,000 “uses up” your BR/HR bands; so, if you have Savings income of £33,000 and dividend income of £10,000, your tax calculation would be as follows:
BR Band – £33,500 £33,000 @ 20% £500 @ 0%
HR Band – up to £150,000 £4,500 @ 0% £5,000 @ 38.1%