C kept everything in simple past.
'They' is used since both husband and wife sipped coffee

There are two clues that they boths sipped coffee:
1) She noticed that he was disoriented while he sipped coffee so presumably she is in his vicinity. She is likely to be sipping coffee also.
2) All answer choices suggest that both of them were sipping coffee:

(A) sipping their coffee
(B) sipping their coffee
(C) as they sipped their coffee
(D) as they were sipping their coffee
(E) sipping their coffee

There is no alternative given in the answer choices to suggest that only he sipped coffee.

thanks both. understand now

Option A
'sipping their coffee the next morning, she noticed that he seemed disoriented'
This Option is definitely incorrect because of the verb concord agreement,remember if the verb of the first sentence is past tense the verb of the second sentence should also be in past tense.
option B.
'sipping their coffee the next morning,he seemed to be disoriented she noticed'
this is a clear bad English because the sentence suffers improper English usage and parallelism.
Option C.
As they sipped their coffee the next morning,she noticed that he seemed disoriented'
THIS IS THE CORRECT ANSWER!!!!
This option is corrected place and all tenses are in perfect past tense which satisfy the Concord agreement rules.
since it all happened it past tense 'sipped', 'noticed', 'disoriented'
Option D.
'as they were sipping their coffee the next morning ,he seemed,she noticed,disoriented.'
This option suffers grammatical error and does not even needs to be evaluated.A blind man could tell this.
Option E.
'he seemed disoriented, she noticed,sipping their coffee their coffee the next morning'
This sentence suffers improper agreement and arrangement of sentence,thus INCORRECT!!!