I am always the first to admit that I have not accomplished everything that I ___________ achieve five years ago.

The given sentence states that the speaker did not succeed in all the aspects or fields that he had planned to, five years ago.
Option (a) is correct, because set out to refers to what was planned or specifically decided, so it fits perfectly into the sentence.
Option (b) is incorrect. Options (c) and (d) are incorrect, because thought means something that was merely considered or contemplated, it does not mean that it was planned or it was the final decision. Also, thought to is a wrong usage of the preposition: to.