Of all the homes on Gotham Street, 1/3 are termite-ridden

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Source: MGMAT Math Foundations

Of all the homes on Gotham Street, 1/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?

Let total homes be H

Termite-ridden = 1/3 (H)
Termite-ridden and collapsing = 3/5(1/3(H)) = 1/5(H)
Termite-ridden and NOT collapsing = 1 - 1/5(H) = 4/5(H). Would this be the answer? Evidently, I am wrong somewhere. Please help!

[RonPurewal]

this problem is not from the CAT exams, so please re-post your query in the "ManhattanGMAT non-CAT" folder.

thanks.