No - not true. The $5,000 does in fact apply as is made clear on the CRA web site (the official source):It seems the 5000$ income does not apply for the first time application.
https://www.canada.ca/en/revenue-agency/services/benefits/apply-for-cerb-with-cra.html#who
The first time application requirements are one item on the list of eligibility requirements. You still need to meet the $5,000 requirement, even if applying for the first time.