What you need to look at is your overall installment loan utilization just before the auto loan was closed and then what it was after that loan reported closed and is eliminated from the equation with only your other 4 installment loans left.
If your installment loan utilization stayed the same or increased, your scores could stay the same or decrease. If your installment loan utilization stayed the same or decreased, your scores could stay the same or increase.
If you're seeing the opposite happen, like your installment loan utilization decreased and your scores also decreased, it means something else changed on your report.
Pretty sure nothing else changed on my report - but I did do the math on the new utilization ratio on my remaining loan balances, and I believe that BBS is correct. Whereas my utilization % was in the 50% range with the auto loan open, with its closure the % recalculated to 67% - and I believe the threshhold for gaining/losing points is 65%? If that's true, then that explains why the score fell so much. It probably dropped a few points from closing the account, but dropped even more from the new utilization ratio.
That being said, I am not sure how that works when we factor in the fact that the EX and TU scores didn't move that much (the TU score recently increased by a few points, actually). That theory also implies that the Fico 9 score is also unaffected by that 65% threshhold. Interesting.