The correct answer is complex sentence.
A complex sentence means that the sentence contains one independent clause (one that can stand on its own), and at least one dependent clause (which is incomplete and cannot stand on its own).
As you can see in the example above, this sentence has one independent clause (I came across my favorite pair of childhood shoes: purple and black jellies with gold buckles.) and one dependent clause (While I was cleaning out my closet the other day...).