Backlink Spam Penalty

I work in a marketing agency providing SEO to companies.

One of the websites I work on had few backlinks, aside from 5000 spammy backlinks from one website.

Do you guys think this will have a big effect? I've submitted a disavow file to search console.

The official line from Google is not to worry. They ignore links they don't like but they don't penalize low quality links with their algorithm. But if you've submitted a disavow file then you've done all you can.