Well, after taking some flack from a post I made a few weeks ago on deer age - I've am posting this link for your reading pleasure. While most of the article gives examples of deer in HF operations, several examples from LF properties are also given - particularly the King ranch.
The facts are that a 5-yo WT buck can really be considered middle-aged, mature but with a LOT more years in him. And a doe may just be getting started at 5yo. There are many factors, of course - not the least of which is good nutrition. But I still contend that shooting a 6 or 7yo just because "he won't live another year naturally" is simply an excuse not backed up by facts.
Note this article does not address peak antler size - but I know more than a few folks with nice ranches that manage/breed their WT with deer that reach their peak at well past 5.5 years - deer that are harvested in the 8,9, and 10yo range with impressive racks not in decline.https://www.qdma.com/articles/whats-the-oldest-deer-on-record