I have a series LR circuit, I apply a DC voltage to it for a time period equal to 5 time constants.

At the end of the 5th tc the inductance is near zero and the only thing limiting current is R.

If the inductor has a ferrite core does the core saturate after 5t if R is low enough?

Seems to me that if current is 99% after 5t then inductance is near zero, which means the core is saturated?

I am sure I am wrong about this but my question is why?