Thomson, the first Australian to win golf’s oldest major, passed away at his home in Melbourne.
He had suffered from Parkinson’s disease for more than four years.
Thomson recorded the first his Claret Jug success at Royal Birkdale in 1954 and made successful defences the next two years at St Andrews and Royal Liverpool.
He regained the title in 1958 at Royal Lytham before claiming his fifth and final success back at Royal Birkdale in 1965.
Martin Slumbers, chief executive of the R&A, said: “It is with great sadness that we have awoken to the news of the passing of Peter Thomson.
“Peter was a true gentleman and will be forever remembered throughout the world of golf as one of the great champions of our wonderful sport.
“He was a distinguished Honorary Member of The Royal and Ancient Golf Club of St Andrews and will be sorely missed by all of us at the R&A. Our thoughts are with his family at this very sad time.”
Thomson was made Commander of the Order of the British Empire (CBE) for his service to golf in 1979 and in 2001 he became an Officer of the Order of Australia (AO).
He was awarded an honorary degree from St Andrews University in 2005 alongside Peter Alliss and Nick Faldo.
“Peter gave me a number of very interesting and valuable thoughts on the game, how it has developed and where it is going which demonstrated his genuine interest and love of golf,” added Slumbers.
“He was one of the most decorated and celebrated Champion Golfers in the history of The Open, winning the Championship five times in total and becoming the only golfer of the 20th century to lift the Claret Jug on three consecutive occasions between 1954 and 1956.
“Our deepest condolences go out to Peter’s wife, Mary, and his four children, Diana, Peta-Ann, Fiona and Andrew.”
Thomson’s compatriot and 1991 Open champion Ian Baker-Finch tweeted: “Australia has lost a golfing legend and my hero.
“My heart felt condolences to his lovely wife Mary, also Deirdre, Andrew, Pan, Fiona and families.
“Peter - my friend and mentor R.I.P. Australian golf thanks you for your iconic presence & valuable guidance over the years.”
Karrie Webb, a former women’s world No 1, said he was an “Aussie legend and true gentleman of the game”.
Paul Lawrie, the 1999 Open champion, wrote on Twitter: “Very sad to hear of the passing of Mr Peter Thomson, 5 X champion golfer of the year but more importantly a true gentleman of the game.”