A lot of those victories came in the confines of the old Stradey Park where New Zealand were famously beaten 9-3 in 1972 and Australia, then world champions, 13-9 in 1992.
But that illustrious chapter in their history closed and a new one opened when they played their first ever match at their new Parc y Scarlets against Munster on November 28, 2008.
And Scarlets skipper and British & Irish Lion Matthew Rees has called on the team to deliver a performance worthy of the occasion against the Heineken Cup champions on Saturday night.
"Being part of this club every player is well -aware of our great traditions, the people that have worn the jersey and what it means.
"It's part of what makes Scarlets rugby unique and the respect that we have players and our supporters have for our great past.
"We also have a lot to look forward to ahead of us as a region, as we can see the progression we are making as a group with so many young players coming from within our system - shown by the make-up of Wales' World Cup team with a number of young Scarlets involved.
"To reach 5,000 games is a huge achievement and one we should celebrate and I know the players will be feeling that when they take on some formidable opposition in Leinster.
"So the more that can come out and support us on this big occasion for us all as a region, the better."
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