Taking into account its structure, this is a compound-complex sentence.
"After a bear cub survived a forest fire in 1950 he became known as Smokey and he lived in the national zoo for many years" is a compound-complex sentence because it contains two independent clauses ("he became known as Smokey" and "he lived in the national zoo for many years") and one dependent clause ("after a bear cub survived a forest fire in 1950"). The two independent clauses are joined by the coordinating conjunction "and" and the dependent clause is introduced by the subordinating conjunction "after". A compound-complex sentence is a combination of a compound sentence, which contains two independent clauses, and a complex sentence, which has a dependent clause joined to an independent clause.