In choice (A), we have an improper modifier, because the word "which," coming after the comma, refers grammatically to the noun before that comma, which would have to be "1975." That's not going to be a sensible reference. We can eliminate choice (A).
In choice (B), the phrase "specializing as his profession" incorrectly equates "grandfather" and "profession," since the word "as" equates. This meaning is incorrect; the grandfather is specializing in something, but he is not himself the specialization or profession. We eliminate choice (B).
In choice (C), the phrase "as a professional" is an appositive phrase (a modifier bracketed by commas) modifying "grandfather," so that usage makes sense. As written, the sentence has only one subject, "grandfather," but that's okay, since there is only one predicate: he "obtained ... and specialized..." Choice (C) looks good.
Choice (D) uses the present verb tense in "specializes," but we know that the verb should be past tense because it describes what happened "then" after a past event.
In choice (E), we have a run-on sentence, because there is no conjunction between the first independent clause (ending with the comma) and the second independent clause (starting after the comma). Both clauses are independent clauses because they have subject/verb pairs and they are not introduced by a subordinating conjunction, such as "because."
The correct answer is (C).