If one maxed out there traditional IRA contribution for 2020 while also putting 5k into their employer 401k plan in 2020, can one rollover the 5k in the 401k into the IRA in 2021 and not have it count against their 6,000 IRA limit?
A 401(k) rollover into a IRA is NOT a new contribution and there are no limits on how much can be rolled over. however, most 401(k) plans prohibit any rollovers prior to retirement or end of employment - check with the plan administrator.
In most cases, you can't move money out of a 401(k) when you are still employed with the sponsoring employer. You can roll over or transfer funds if you quit, are terminated, or are fired. Some employers may allow a hardship withdrawal, but you can't use hardship as a reason to do a rollover.