Why is disadvantage not the rough equivalent to -5? The PHB lists the value as 5 for passive checks from advantage/disadvantage.

From

here, where they crunch the math, "The general rule of thumb that in the mid range of the d20 (from success on a 9+ to 12+) advantage grant roughly a equivalent to a +5 bonus and disadvantage a -5 penalty. "

and

"The PHB provides a short cut for applying advantage via a +5 modifier to supplant the roll. Coincidently

6.650 - (6.650-3.325)/2 = 4.9875 ~ 5"

Well, as I said, it's technically incorrect. For starters, you can't map a triangular distribution to a flat bonus without losing lots of information (which you are). Secondly, the impact is not the same. If the disad target needed an 16 to hit you, shield makes you unhittable except on a crit, but disadvantage does not (it reduces your chance of being hit from 4/20 to 16/400, or from 20% to roughly 4%. This is actually a titch better than shield in this regard. If the target can only hit you on a 20, shield does nothing for you, but disadvantage makes the odds of hitting you go from 5% to 0.25%.

On the other side, if the target needs a 7 to hit you, shield changes your chances of being hit from 70% to 45%. Disadvantage changes those chances from 70% to 49%, or almost a full "point" less than shield. This is, of course, misleading again, because shield doesn't protect you from crits, but disad does no matter what the target number needed is by strongly reducing the chance of a critical hit.

On to the mean! The mean of advantage is 13.82 with a standard deviation of 4.71. This means that roughly 67% of all rolls with be between an 18 and a 9. Contrasted with a straight d20 with a mean of 10.5 and an sd of 5.77, making 67% of all rolls between 5 and 16 (which is 13/20 options or 65%, so, duh). The difference at the edges is 4 at the low end and 2 at the high end. This doesn't at all look like a flat +5.

And, while at exactly 10, the chances of rolling at least a 15 on advantage vs a straight +5 matches very closely, it quickly diverges. By the time you get to the chance for rolling a 21, they're infinitely far apart. This does, however, illustrate the +5 to passive rolls mechanic of advantage -- considering that you're assuming a roll of a 10 already, this is a very quick and fairly adequate shortcut, but it holds only on assumed rolls over time (like passive scores are meant to represent). If you actually roll, the differences are quickly apparent.

So, yeah, it's technically wrong on many counts, but it's also misleading because the +5 comparison only holds in specific circumstances in a very narrow range (pretty much 9-12) and if you're far outside this (like say near 18) it's an assumption that will mislead you pretty badly as to what your actual chances are. It needs to die as a meme.