Five Presidents

Since he also served about six weeks before 1964, I'm going to mention Lyndon B. Johnson, in the first group, only because of his "Senate knowledge", since he also was Senate leader and presiding officer as VP. In addition, I would have Thomas Jefferson, James Madison, Grover Cleveland, and Harry Truman, in that group, and have George Washington, John Adams, and Abraham Lincoln as advisers to the Board of Advisers, as well

The ones I would not want on that board, include Millard Fillmore, Franklin Pierce, James Buchanan, Warren Harding, and U. S. Grant, arguably the worst Presidents our nation ever had, unless the subject being debated was strictly the military, in which case I would have U. S. Grant right at the "top of the heap", along with Dwight Eisenhower, Andrew Jackson, George Washington, Zachary Taylor, and Theodore Roosevelt, all of whom were among those that knew a couple of things about the Army, at least. :thumbs:

I would cut a bit of slack for Presidents James Madison, Abraham Lincoln, Woodrow Wilson, Franklin D. Roosevelt, and Harry Truman, in one instance, all of whom wound up having the thankless and impossible task of dealing with large wars, which were not of their making, and definitely not of their preferred choosing, just as some later Presidents that I cannot mention, in accordance with the OP.

Subjects should include "a more perfect union", "justice", "domestic tranquility", "the common defense", "the general welfare", and " providing the blessings of liberty"! Sorry, I hit more than five, in a couple of instances. :saint:

[Edited to add] I would also have Calvin Coolidge as a Senate Advisor, in all instances, here. Think about it! The Senate currently has 100 members, at least 3/4 of whom could take some very good lessons from "Silent Cal"!

Ed