IMO B

I chose the above because of parallelism.

Out of B/D i will go with B.

Usage of like is wrong in A C E. D lacks parallelism.

A

ing should be consistent

[spoiler]B for me. What is the OA?[/spoiler]

imo: b

Building on civilizations that preceded them in coastal Peru, the Mohica developed their own elaborate society, based on cultivating such crops like corn and beans, the harvesting of fish and shellfish, and exploiting other wild and domestic resources.

(A) based on cultivating such crops like corn and beans, the harvesting of fish and shellfish, and exploiting - firstly wrong idiom "such crops as" not like, secondly the phrases are not parallel "cultivating...., the harvesting" - the first phrase starts of with a verb and the second is a gerund.
(B) based on the cultivation of such crops as corn and beans, the harvesting of fish and seafood, and the exploitation of - Looks parallel, all are nouns followed by preposition (noun-prepositional phrases) . Also "such as" is used to quote examples
(C) and basing it on the cultivation of crops like corn and beans, harvesting fish and seafood, and the exploiting of - "crops such as corn and beans" is to be used when you are referring to examples of crops. Not parallel - "The cultivation... harvesting..." .The first is a noun phrase and the second is a verb and doesn't go well with "basing it on harvesting fish"
(D) and they based it on their cultivation of crops such as corn and beans, the harvest of fish and seafood, and exploting - Not parallel, the first two phrases are noun phrases while the last phrase starts of with a verb.
(E) and they based it on their cultivating such crops like corn and beans, their harvest of fish and shellfish, and they exploited - "such crops like" is wrong. Parallelism is in the wrong place. "Building on civilizations..., the Mohica developed .... and exploited....". It hould be parallel with "cultivation.... the harvest...and the exploitation..." to aid in how the society was built.