5:8a Let it be known to the king that we went into the province of Judah, to the house of the great God.

We (excl.) want to inform the king that we went to the region/area of Judah to the temple of the great God.
-or-
⌊Your Majesty,⌋ we ⌊your servants⌋ went to the house of the powerful God ⌊of Israel⌋ in the land of Judah.

5:8b The people are rebuilding it with large stones, and placing timbers in the walls.

The temple is being built with huge stones, and wood is being set in the walls.
-or-
The builders are repairing it using big, ⌊cut⌋ stones, and they are placing ⌊layers of⌋ wooden beams/planks/boards in its walls.

5:8c This work is being carried out diligently and is prospering in their hands.

The work is being done very carefully/thoroughly and is progressing/succeeding quickly through their effort.
-or-
They are doing excellent and rapid work.

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