Why would trading in an ETF’s underlying stocks be required if investors were to sell enough shares?

Your quote is incomplete. It says

FactSet measures how much trading in an ETF’s underlying stocks would be required if investors were to sell enough shares to prompt the redemption of 5 per cent of assets under management.

That means:

• If investors sell very many shares of an ETF, more than are bought, they get under price pressure.
• Thus, an authorized participant (AP) buys them and redeems them, i. e. turns them into the basket of securities they consist of (the "underlying securities"). Afterwards, these underlying securities are sold at their market price if the AP doesn't want to hold on them. This is "trading in an ETF's underlying stocks".

(This process works in the opposite direction as well, but let's focus on this one here.)

The sentence in the quote now refers to this process and talks about the situation where investors sell so many ETF shares that the AP redeems 5 per cent of the AUM, i. e. 5% of the ETF's total value. (That's quite a lot.)