No, because the rule is "5 failures per account, per hostname, per hour".
This is 5 failures on that account, but only 1 failure on each hostname.
The purpose of this limit is not to penalize you for having a very large number of web sites and being unlucky with random failures! It's mainly in place to prevent people from retrying the same request when it fails repeatedly.
The most commonly-encountered Let's Encrypt rate limits both tend toward this general goal: If you get a failure, please investigate why that failure happened and try to fix it before trying that same thing again, instead of making the same kind of request many times in a row.