Five and twenty is the Germanic form of building numbers. This is still used today in most Germanic languages. It used to be the norm in old English too. This probably only changed due to the influence of Norman-French on English. The switch was gradual and it is assumed that it started with the high numbers. By 1700 or so the French way was the norm except, and this is the relevant part to your question, in some dialects and when saying your age as well as the time. This was still somewhat common in the 19th century.

Funnily enough, since the Count of Monte Cristo is originally a French novel the original has the number order in exactly the way modern English would have it. For example, in this passage "Le bruit des pas fit lever la tête à une jeune femme de vingt à vingt-cinq ans,..." So whenever the old-timey five and twenty structure is used, this was a deliberate choice of the translator. In the copy on google books I found, which handily has a page by page comparison of French and an English translation from 1845, the translator uses sometimes one way and sometimes the other. Unfortunately I can't tell you what motivated his choices.

My sources for the first paragraph are a German article which references the following sources: WEINSTOCK, Horst (1999) Historical and comparative aspects of numerals between twenty-one and twenty-nine. In Uwe Carls und Peter Lucko (Hgg.), Form, function and variation in English: Studies in honour of Klaus Hansen. Frankfurt: Peter Lang, S. 65–77.

My source for the second paragraph is this copy of the Count of Monte Cristo.