[lord farquaad]

I named this molecule (picture attached) 4-chloro-5-methylcyclopentan-2-ol. When checking my answers, the given answer was:
4-chloro-5-cyclopentylhexan-2-ol

How would someone know that the cyclopentane is not directly attached to the carbon chain on the fifth carbon?
How can naming show that the fifth carbon is attached to another carbon that is part of the cyclopentane?

Could it be named: 4-chloro-6-cyclopentyl-5-methylhexan-2-ol? Or does that not work because the longest parent chain is not named properly?

[Orcio_87]

Could it be named: 4-chloro-6-cyclopentyl-5-methylhexan-2-ol?

No, because:

1. cyclopentyl is a substituent at 5, not 6 carbon atom.
2. there is no -CH₃ substituent at this hexane derivative.

[mjc123]

How would someone know that the cyclopentane is not directly attached to the carbon chain on the fifth carbon?
How can naming show that the fifth carbon is attached to another carbon that is part of the cyclopentane?

Because that is what "cyclopentyl" means. The cyclopentyl group is a cyclic C₅H₉ unit attached by a single bond (not part of the ring) to another atom. "5-cyclopentyl" does not mean that C5 of the chain is included in the cyclopentane ring. The compound you appear to be thinking of would be 4-chloro-4-(1-methylcyclopentyl)butan-2-ol.