SQL Server native log backup running every 5 minutes
Will the next log backup be initiated after 5 minutes or will it be waiting for the log backup to complete.

If the log backup is run by SQL Server Agent
If the scheduled time comes up and the prior instance of the job is still running, it will postpone until the next scheduled time. Two instances of the same job can not run at the same time.
If the log backup is run by some other scheduler software
You'll have to check with your vendor's documentation or support team, but I can't imagine any software allowing this to behave any differently than SQL Server Agent, unless they have an option to not skip collisions and queue them up, and you have enabled that option.