So, If I get this right. If a weapon has both 10' and 5' attack, like the spiked chain, moving out of the 10' range to adjacent to the opponent at 5', is technically moving out of the further threatened square into another threatened square, and therefore provokes A.

.? Because that would be cool.
That is correct. Every time a foe moves out of a threatened square, an attack of opportunity exists.
Consider, Ralph ("R")and his longsword, with the 5' reach....
ABC
DRE
FGH
Let's say Ralph is fighting Bob, and Bob is in square "B". Then, Charlie, Bob's ally, moves past the two of them. Charlies moves through squares C, E, and H, right past the two of them.
This creates three Attacks of Opportunity for Ralph.
AoO 1 - As Charlies leaves square C.
AoO 2 - As Charlie leaves square E.
AoO 3 - As Charlie leaves square H.
The Attack of Opportunity is provided just before Charlie leaves the square, so Ralph could take his AoO on Charlie when Charlie was in square C, E, or H.
Now, characters are limited to only one AoO per round unless the character has a Feat that says otherwise.
So, if Ralph doesn't have Combat Reflexes and a high DEX, he's only getting one AoO in a round. Provided he hasn't already used his one AoO in this round, Ralph could take the AoO on Charlie in any of the three squares C, E, or H.
AoO's work the same with reach weapons.
ABCDE
FGHJK
LMXNO
PQRST
UVWYZ
X = Character with Reach weapon that threatens 10' away. He threatens the ABCDE, EKOTZ, UVWYZ, AFLPU ring.
Let's say X has initiative and prepares a ready action for a foe to attack him. The foe is coming straight for him, through square C to square H to engage X in melee.
This means X would get two attacks. His Ready Action is tripped when the foe approaches, so that's one attack. And, X gets an Attack of Opportunity on his foe when the foe leaves square C.
If X's weapon threatened both 10' and 5' around the character, and X had the Combat Reflexes Feat and a DEX of at least DEX 14, then he's till only get 2 attacks.
He's get one when his Ready Action was tripped.
He'd get his first Attack of Opportunity as his foe left square C.
Even though he's got Combat Reflexes and a DEX with a +2 modifier, he doesn't get the attack of opportunity on the foe in front of him until the foe leaves the square.