... 25

Officially, 25 was the minimum age at which a man could be ordained as a priest/parson/rector/vicar/curate/whatever you want to call him. There was also a rank of "deacon" which you could take at 23, but since a deacon is only really a church assistant, I don't think that this counts. I have never found any instances of men younger than 25 being allowed to take up a living, and since it wasn't just the decision of the holder of the advowson- as old Mr Darcy was- but also required the assent of the local Bishop, I believe it was a rule which wasn't broken.

My reference for the "25" age barrier is Irene Collins's Jane Austen and the Clergy which I thoroughly recommend as a fascinating analysis of what it was like to be a clergyman, or live with a clergyman, in Jane Austen's time.