This question is testing PARALLELISM and SUBJECT/VERB agreement.

When there is a closed parallel marker such as BOTH X AND Y, the part of the sentence that follows "both" must be parallel to the part that follows "and."

In each of the answer choices, I've highlighted what comes after each marker:

A. is both unhealthy and cost a lot of money
Not parallel - both [adjective] and [verb]

B. are both unhealthy and costs a lot of money
Not parallel.

C. are both unhealthy and cost a lot of money
Same.

D. is both unhealthy and costs a lot of money
Same.

E. is both unhealthy and costly
Both [adjective] and [adjective] - correct!

We also could have used SUBJECT/VERB agreement to eliminate answer choices. "Smoking" is singular, so we cannot use "are" or "cost." That would have eliminated A, B, and C.

The answer is E.

This two-part parallelism - also known as CLOSED PARALLELISM - is very common on the GMAT.
Any time you see the following:
BOTH ____ AND ____
EITHER ____ OR ______
NOT ONLY _____BUT ALSO _______
NOT ________ BUT _________
etc,

... you need to make sure that what comes right after the first part structurally matches what comes after the 2nd part.

For more, see:
https://www.beatthegmat.com/parellelism ... tml#796027
https://www.beatthegmat.com/help-manhatt ... tml#713882
https://www.beatthegmat.com/sc-question- ... tml#769597
https://www.beatthegmat.com/spanish-arma ... tml#775935
https://www.beatthegmat.com/og-pg-725-81 ... tml#767953
https://www.beatthegmat.com/think-of-x-a ... tml#575578
https://www.beatthegmat.com/most-expendi ... tml#716319