RAW, the Paladin would have a monk AC/Damage bonus of monk level 5 because he doesn't have 'Monk levels', he has an unarmed strike that gains a bonus that references Monk levels.
That being said, I believe most would homerule it as +1 AC (Monk level 5) and unarmed damage based on 1/2 Paladin levels + 5 because other cases of gaining a class ability treat you as having that class ability for Feats and anything else.
Archetype: If an archetype replaces a class ability with a more specific version of that ability (or one that works similarly to the replaced ability), does the archetype's ability count as the original ability for the purpose of rules that improve the original ability?
It depends on how the archetype's ability is worded. If the archetype ability says it works like the standard ability, it counts as that ability. If the archetype's ability requires you to make a specific choice for the standard ability, it counts as that ability. Otherwise, the archetype ability doesn't count as the standard ability. (It doesn't matter if the archetype's ability name is different than the standard class ability it is replacing; it is the description and game mechanics of the archetype ability that matter.)
Example: The dragoon (fighter) archetype (Ultimate Combat) has an ability called "spear training," which requires the dragoon to select "spears" as his weapon training group, and refers to his weapon training bonus (even though this bonus follows a slightly different progression than standard weapon training). Therefore, this ability counts as weapon training for abilities that improve weapon training, such as gloves of dueling (Advanced Player's Guide), which increase the wearer's weapon training bonus.
Example: The archer (fighter) archetype gets several abilities (such as "expert archer") which replace weapon training and do not otherwise refer to the weapon training ability. Therefore, this ability does not count as weapon training for abilities that improve weapon training (such as gloves of dueling). This is the case even for the "expert archer," ability which has a bonus that improves every 4 fighter levels, exactly like weapon training.