Rolls needed given a six precedes any five

A fair die is rolled repeatedly until the first $6$ shows up. Conditional on no $5$ having appeared before that first $6$, what is the expected total number of rolls?

$3$. Let $T$ be the first roll showing a 5 or a 6; $T$ is geometric with success probability $\tfrac13$, and whether that roll is a 5 or a 6 is independent of $T$. Conditioning on it being a 6 makes the total number of rolls equal to $T$, whose mean is still $3$. (Simply deleting 5s from the die and answering 5 is a common mistake.)