The correct option is
A didn't answer/was taking
Option A is the correct answer because the statement is in simple past tense, so it is correct to say "didnot answer" because"did" is the past tense of"do" when used as a first or second person form.
"was taking" is correct because in the simple past tense, the speaker is describing the instance when he "was taking" a shower, "was" is the past tense of "is", hence it is correct.
Option B is incorrect because "did" is the past tense of "do" and so did should be used.
Option C is incorrect because "does not" is used in plural forms, and in the present form, while "did" is the past form and so is correct.
Option D is incorrect because it is future tense while the statement is in future tense.
Option E is incorrect because "am answering" means that the speaker has decided to answer the call, which is incorrect because the statement demands a reason for taking the call.