1. The radio is out of order.

2. The radio doesn't work.
3. The radio is out of work.
4. He is out of work.
5. He is unimployed.
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#1 is #2, right? What about #3? Does #3 mean #1? Does #4 mean #5?

3 is wrong. The others are correct.

Yes, 1 and 2 mean the same. 4 and 5 are the same.