1. The sun having set, we started for home.

2. After the sun had set, we started for home.

3. Because the sun had set, we started for home.
-----------------------
Does #1 mean #2 or #3?

4. The sun set, so we started for home.
5. The sun had set, so we started for home.
(Which one is correct? Are both correct?)

In this context, all of the sentences (#1, #2, and #3) convey the same meaning. They indicate that we began our journey home after the sun had already set. The slight differences in wording do not significantly change the overall meaning.

Similarly, in sentences #4 and #5, both versions are correct and convey the same meaning. They both imply that because the sun had set, we commenced our journey home.

Overall, all of the sentences indicate the same sequence of events: the sun had set, and as a result, we started heading home.