5th = US Amateur
6th = British Amateur
Kevin, I'm always amused when golfing traditionalists try to suggest that modern amateur championships are at such a level. They simply aren't - how many players players in last year's US or British Amateur would be amongst the top 100 players in the world?
They mattered in Bobby Jones' day, because there were fantastic players who never turned professional. The amateur championships had good fields. Now any kid who can get the ball airborne is a pro by 23.
Just a question for the non-traditionalists. When did the AMateurs stop being majors? When Jones was winning them they counted. When Palmer and Nicklaus were chasing Jones' record of 13 majors they counted. They counted for SI in 1978 when Jack won Sportsman of the Year and at the time had 17 majors. The NY Times counted them when Jack was on his march to break Jones' record. In the 1986 Masters telecast more than one reference to Jack's 20th major is made so they counted then.
Then a phenom (who happens to be black) comes along and is on the cusp of breaking Jack's records and would be closer if Amateurs "still" counted and yet someone decides THEN, no let's not count those. What gives?
I also think that by not counting Amateurs it gave some writers the chance to talk about Mickelson, O'Meara not having "majors" until they broke through . BTW Sergio would have a major if AMs counted but it's a better story to say he is "majorless" isn't it? (Come to think of it in his case maybe they shouldn't count 
).
If we belabor the point certainly the Western Open was a major for some time in its history and the Open Championship should have certainly lost its major status for a while anyway since there were times when none or very few of the best players competed in that as well. The Masters must also be glad strength of field isn't what (alone) makes a major.
But back to my original question. When did Amateur Championships stop counting as majors? For extra credit, who decided and why? 
I will give one theory why the two Amateur Championships do not hold "major" status any longer.
Going back to 1981 three people have won the US Am, and then gone on to win a professional major (Tiger Woods, Phil Mickleson, & Justin Leonard). Where as, from 1953 to 1980 eight of the men who won US Ams went on to win professional majors.
Since World War II, Jose Marie Olazabal is the only person to win a British Am, and go on to win a professional major. That was in 1984. Since Jose’s win, Sergio Garcia is the only other British Am winner to have more than one win on the European or US tours.
In the last 22 Masters, only six winners have no more than one major title. In the last 21 US Opens, only six winners have no more than one major title. In the last 17 Opens, only six winners have no more than one major title. Finally, in the last 15 PGAs, only six winners have no more than one major title.
Before World War II most winners of the Ams where lifelong Ams. Robert Jones was the only Am to really dominate the pros. In current times the best golfer will always be a professional. Since Jones was THE dominant player for many years, and considered one of the best to every play, his full record was compared to any others also considered as one of the best. Therefore for players like Jack Nicklaus and Arnold Palmer, the Ams counted. Once a golfer (Tiger Woods) finally arrived to be a true successor to Nicklaus as the next possible "best ever", the Am did not appear to be an accurate way to evaluate greatness.
One would think just the opposite would occur, that since Tiger also dominated the amateur ranks, and passed Nicklaus on number of US Am titles, that the current sports media would want to count Tiger's three Ams. Perhaps the fact that Tiger ignored making any real effort to get a British Am title resulted in some concluding that the Ams no longer mattered when counting "majors". I think it is more likely that since before Tiger the prior 19 winners of the US Am included only won winner of a professional major may have been the biggest reason the media stopped counting Ams. And that one winner was Hal Sutton, who won his Am in 1980, then won the 1983 PGA, but by the time Tiger arrived appeared to have had a disappointing career. Since the Ams for almost 2 decades before Tiger had not been a precursor to greatness in the pro ranks, the major media had stopped thinking about the Ams and thus never considered looking at the Am counts when looking at the records that Tiger would be facing. Since Tiger has dominated all in golf since 1997, the Ams no longer count as majors and likely never will again.
By the way, although Phil, Leonard, and O'Meara all won Ams before Tiger, they had not yet won any majors before Tiger's 1997 Masters win.
On a final note, Dan Jenkins once proposed that Ams should only count as majors once that player also wins a professional major. Therefore Hal Sutton, Justin Leonard, Lanny Wadkins, Jerry Pate, and Craig Stadler now have 2 majors each. But Sergio Garcia, Scott Verplank, and John Cook still have no majors. Per this system, Tiger now has 17, and Nicklaus has 20. Most amazingly John Ball moves from a tie for 77th (among most wins in the four professional majors) to a tie for 5th (nine: 1 Open Championship + 8 Amateur Championships) among the list of most wins in all six "majors". 76 players have won multiple professional majors and only seven of them have won one of the two Ams (Robert Jones, Arnold Palmer, Jack Nicklaus, Mark O’Meara, Jose Marie Olazabal, Phil Mickelson & Tiger). Of the 119 men with just one professional major win, only 12 of them have won either of the two Ams.