The correct answer is C. I’ll be in bed.
The other options are incorrect because they do not accurately reflect the time that is being referred to. Option A, I’ve been in bed, is incorrect because it implies that the speaker is currently in bed. Option B, I’d been in bed, is incorrect because it implies that the speaker was in bed at some point in the past but is not currently in bed. Option D, I was in bed, is incorrect because it implies that the speaker was in bed at some point in the past and is not currently in bed.
The correct answer, C. I’ll be in bed, accurately reflects the time that is being referred to. The speaker is saying that they will be in bed at 5 o’clock tomorrow morning. This is a future event, so the correct verb tense to use is the future tense.