I shall provide you with an explanation of the usage of "would have" in this context:
The idiom at issue here is "would have", which is the construction used to form "The past conditional"! This conditional is expressed using the modal "would" before a past infinitive (= "have" + past participle). This construction serves to express missed opportunities and past hypotheses:
1) "She told me that she would have liked to come and see us.
In your position, I would have done the same thing".
2) "If I had had the opportunity, I would have told her the truth".
3) "If he had worked harder, he would have received a better grade".
4) If he had delivered the money he took, his mother would not have been angry with him".
So, in the context you provided, the idea conveyed is that "(even if he had had the opportunity - five years ago or even one) he would not have said this to anyone." = that is, there was a period when he would not have told anyone about his condition, even if he could. HOWEVER, NOW, he is able to talk about it!
** NOTICE: Sometimes the "If" clause is omitted from the clause - the construction of ir is implies, however. You must study and learn more about the The Past (Unreal) Conditionals in order that you can be able to notice whenever a sentence conveys the idea of a hypothesis or a missed opportunity regarding a past period.
Hope you have understood! :)