Dont think there is any rule that say advantage gives you +5 to the relevant role
Check again. Advantage on a passive check gives you a flat +5; disadvantage -5. Again, only to passive checks.
Basic Rules said:
Here’s how to determine a character’s total for a passive check:
10 + all modifiers that normally apply to the check
If the character has advantage on the check, add 5. For disadvantage, subtract 5. The game refers to a passive check total as a score.
(I am aware, however, that it is apparently demonstrable that rolling 2d20, taking the higher result averages out to a value around 5 higher than merely rolling 1d20; but I dont think it is a rule or a variant rule, maybe a variant rule).
Not quite. If you're looking at it as a success increase, then the maximum delta is when you need a 10-11. This increases or decreases your odds of success by 25%, respective to ad/disad. Often, this get's shorthanded to +5, but this is, strictly speaking, incorrect. Useful, though, and why oassive checks, which are based on rolling a 10, use the +/- 5.
The further towards to top and bottom tge DC, though, the less delta ad/disad has, although the relative change is. Even if you shorthand to +/-, which is even more incorrect at the extremes, it diesn't average to +5.
Also, passive perfeception is you and your (untrained) Bassett hound happily, if not aloofly, walking down the street... Compare to the hunting dogs sniffing out that duck in the pond; or the bloodhound tracking the fugitive..
No, passive checks aren't distracted -- that's what disadvantage represents. Passive checks are repeated or sustained efforts. It's a tool of convenience so you don't have to roll hundreds of checks when looking out for traps going down a long dungeon corridor, not representative of a neutral state. If you're not doing the thing at all, you don't get a passive check for it.
From the basic rules:
Basic Rules said:
A passive check is a
Special kind of ability check that doesn’t involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for
Secret doors over and over again, or can be used when the GM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.