first

I presume you mean chapter 2 example 5 and you are referring to the use of the 0% starting rate for savings income. This is ONLY available on taxable savings income that falls within the first £5,000 of TAXABLE INCOME. Thus if taxable NON savings income exceeds £5,000 there is no 0% starting rate available to apply to any taxable savings income.
In example 5 the taxable non savings income is £1,000 meaning that only £4,000 of the taxable savings income falls within the first £5,000 of taxable income and therefore benefits from the 0% starting rate