Two vowels on the first guess, with the E out of position. Two vowels is usually all that's needed, so in guesses 2 and 3 I'm trying for consonants, while putting the E in new locations.
After guess 3 I haven't picked up any consonants, but I know the E is in position 5. With an A at the front and an E at the end, I figure there must be a vowel in the middle. I is still open, so I try ABIDE - with no luck.
The missing vowel in the middle is almost surely an A. With my remaining letters, I can think of four possibilities (AGAVE, AGATE, AGAPE, AMAZE), but I only have two guesses remaining. PIVOT, guess 5, is an elimination word. If the word is AGAVE, AGATE, or AGAPE, I'll get a hit on P, V, or T, whichever is correct. And if PIVOT misses entirely, then the word must be AMAZE. PIVOT gives me a P, so AGAPE it is.
Whew!!!