17:5a So Elijah did what the LORD had told him,

So Elijah did what Yahweh had commanded/instructed him to do.
-or-
Elijah obeyed the command/instructions of Yahweh.

17:5b and he went and lived by the Brook of Cherith, east of the Jordan.

He went to stay/live by the Kerith Wadi/Stream, east of the Jordan River.
-or-
He went/crossed to the east of the river Jordan. There he remained/lived at the creek/stream called Kerith.

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