My reasoning below:
The health benefits of tea have been the subject of much research; in addition to its possibilities for preventing and inhibiting some forms of cancer, the brewed leaves of Camellia sinensis may also play a role in reducing the risk of heart disease and stroke.
A. in addition to its possibilities for preventing and inhibiting - incorrect formation - 'to' prevent or inhibit - prevent and inhibit cannot happen together
B. in addition to its possibilities to prevent or inhibit - isolated its correct, but not parallel to 'reducing'
C. besides the possibility that it prevents and inhibits - not parallel to reducing
D. besides the possible preventing and inhibiting of - awkward - 'inhibiting' of
E. besides possibly preventing or inhibiting - parallel and concise with the addition of 'or'

E is the answer as it is concise and uses good language
A is wordy and "its" is ambiguous
B again " its " is ambiguous and use of infinitive is not correct .
C it is ambiguous
D we have to use nouns here we have gerunds so not correct .
E correct
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Two sentences can be connected with ";"

Sentence-1: The health benefits of tea have been the subject of much research
Sentence-2: in addition to its possibilities for preventing and inhibiting some forms of cancer, the brewed leaves of Camellia sinensis may also play a role in reducing the risk of heart disease and stroke.

Sentence-2a: "in addition to its possibilities for preventing and inhibiting some forms of cancer" - Modifier
Sentence-2b: "the brewed leaves of Camellia sinensis may also play a role in reducing the risk of heart disease and stroke." - Main clause

ITS possibilities --> whose possibilities?? so here you look for the subject of the "ITS"

but subject of main clause is "the brewed leaves of Camellia sinensis" i.e. LEAVES and "leaveS" is plural. so "its" referring to plural subject "leaveS" is incorrect.

look for this issue in all other sentences - A, B & C all of these choices are wrong for this reason.

Now who is doing the action preventing or say inhibiting? -- Leaves

so choice E correctly uses the structure "verbing...,subject"

Now beware of choice D here because it fools you with "THE PREVENTING OF", which is not VERBING.

Now there are other flaws as in choices but i was able to get to the righ answer with simply the above issues.

Hope it helps.
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Imo E
It is short and concise .
Also
Preventing or inhibiting modifies tea .
B is long and its is ambiguous

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Guys E is correct because it is grammatically correct and between B and E, E is more concise. Concision is often favored on the GMAT. But that doesn't necessarily mean the most concise answer choice is correct- the most concise answer choice that is both logically and grammatically correct.

It either prevents or inhibits... Both can't be done together and it's illogical to say so.

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prevent or inhibit correct
prevent and inhibit incorrect
You cannot 'both' Prevent And Inhibit something at the same time, logically.

between B and E.
In B "its" is awkward.
‘its’ is referring to the ‘brewed leaves of Camellia sinensis’ when it should refer to ‘tea’ .
Also You will realise that it refers to Brewed Leaves: Plural. So, "It" cannot refer to "Leaves."

GMATNinja - could you please clear this?
in the later part of the sentence, I see an "ing" form and so answer will be among A,D and E..
what is wrong in D?

E- possibly is an adverb and it can modify only adjective, adverb but preventing?

The health benefits of tea have been the subject of much research; in addition to its possibilities for preventing and inhibiting some forms of cancer, the brewed leaves of Camellia sinensis may also play a role in reducing the risk of heart disease and stroke.

(A) in addition to its possibilities for preventing and inhibiting --> pronoun error
(B) in addition to its possibilities to prevent or inhibit
(C) besides the possibility that it prevents and inhibits
(D) besides the possible preventing and inhibiting of
(E) besides possibly preventing or inhibiting --> correct