This is a complex sentence because you have one dependent clause, “without disturbing anyone,” followed by an independent clause, “we slipped out the back door.”
Simple sentences = one independent clause.
Compound sentence = two or more independent clauses.
Complex sentence = one independent clause and at least one dependent clause.
“Without” is a preposition, meaning that the clause before the comma starts with a prepositional phrase, and prepositional phrases are incomplete thoughts that can’t stand alone in a sentence. However, independent clauses can stand alone in a sentence, so you would be able to say, “We slipped out the back door” by itself.
