Man, sensible, admitting Henry (5)

I believe the answer is:

shane

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'man' is the definition.

'sensible admitting henry' is the wordplay.
I cannot really understand how this works, but
'henry' could be 'h' ('H' can be a synonym of 'henry') and 'h' is located in the answer.
'sensible' could be 'sane' (I've seen this before) and 'sane' is located in the leftover letters.
This accounts for all the letters.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Times.

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