Tsunade graduated from the Academy at 6, so yes, she was in fact a ninja at that point in time.
And yes, I do know that's what Kishi MEANT to say, but I'm not gonna take his word for it. After all, why should I ignore the canon timeline just because Kishi made a retarded blunder? I'm not going to accept Kishimoto's words by what he means to say, I'm going to accept them by how he says them and how he presents them.
He ****ed up in this case, thus canonically confirming 5 Y/O Tsunade to be on par in strength to Yin Seal Sakura. I don't care if it was unintentional or an accident, what's in the manga is in the manga, as VS debates are through inverse perspective.
And before you bring up nonsense like ''Well, I guess that means Itachi IS invincible", the difference here is that that has been disproved while 5 Y/O Tsunade being on par with YS Sakura has not been. Not to mention anyone can tell the difference between a comparison and a Hyperbole