Answer: Complex sentence.
Step-by-step explanation: a complex sentence is a sentece formed by an independent clause (a phrase that has complete meaning on its own) and at least one subordinate or dependent clause (a phrase that doesn't have completin the given excerpt meaning on its own). In the given sentence we have a subordinate clause: "While I was cleaning out my closet the other day" and an independent clause: "I came across my favorite pair of childhood shoes: purple and black jellies with gold buckles."