Translation:I closed the window, and left the house.
What’s happening here is that you can’t have a -ta verb in the middle of a sentence. You can have a -te form verb, which implies a sequence of events, and when translated into English takes the tense of the last verb in the sentence. In this case でました is past tense so you know しめて is past tense, too.
You can use the -masu stem or the -te form to connect two sentences, but the -masu stem is mainly only used in literature so you wouldn't hear it in speech.
in written Japanese (including in articles, books, and song lyrics), stem form verbs can be used to indicate “and”:
Inu o tasuke, ie ni kaerimashita.
I helped the dog, and went home.
This use of stem form is similar to one of the uses of –Te Form