Here is a passage and note extracted from here:-
“By the time Shakespeare gets to the last of his history plays concerning the Wars of the Roses*, HENRY V, the party boy who would be king has become a man. . .”
“*Shakespeare wrote eight plays dealing with the Wars of the Roses during which time the crown passed back and forth between the House of York and the House of Lancaster. Henry VI, Parts 1, 2 & 3 and Richard III make up the second half of the story, but Shakespeare wrote this section first. He would later go back and write the first half of the story in Richard II, Henry IV Parts 1 & 2, and Henry V. . .”
I don’t know that I consider Shakespeare’s Henry IV and Henry V to be about the Wars of the Roses as such. Surely the wars began with Henry VI? Henry IV and Henry V are concerned with the first portion of the 15th century, well before the conflict. It’s like saying that plays about Queen Victoria and Edward VII are set during World War II. But then, I’m probably nit-picking.
You are right. Henry V (and his time) was still part of the 100 year war, not the what we call the War of the Roses.