Having only watched some the first 5 seasons of TNG I was wondering if there is any reference to how long Klingons live? During the series I haven't heard any reference to how old Worf is.
Klingons tended to live for over 150 years, but even into advanced old age, they tended to still be strong enough for combat. (DS9: "Blood Oath")
However, their maturation also happens at different rates than humans. In DS9 6x03, Sons and Daughters, Worf's son returns, appearing older than he should:
Many fans felt that Alexander was far older in this episode than he should have been given his age as established in The Next Generation. Bradley Thompson countered this argument by pointing out that it has never been established how fast Klingon children grow.
Alexander was born in 2366 and that episode takes place in 2374, making him about 8 years old and already a member of the Klingon Defence Force.
As for Worf in particular, he was born in 2340, making him about 24 years old during TNG Season 1 (2364), and about 28 years old as of TNG Season 5 (2368).
No quotes for Klingon lifespan were ever directly mentioned in the show. Most of the time we are left to infer how old Klingons could be.
Quoted directly from Memory Alpha:
Klingons were capable of living well over a century in age. Individuals such as Kang, Koloth, Kor and Arne Darvin lived well over one hundred years. (DS9: "Blood Oath", "Trials and Tribble-ations", "Once More Unto the Breach")
No exact lifespan has been given for Klingons, just approximates. In 2370, Odo observed that Kor "must be a hundred years old" and his "best friend," Koloth, was "probably a hundred and fifty years old." This observation was made over 100 years after their encounter with James Kirk.
Klingons have physiological advantages over Humans in terms of physical strength, stamina and resilience. Even though Humans and Klingons share a genetic progenitor in the distant past, the Klingon homeworld was more challenging giving the physical advantage to Klingons.
A longer lifespan would be an evolutionary asset and likely an aspect of the evolutionary forces which acted on their their genome from the challenges in the Klingon environment.
In addition to any normal environmental advantages, it is also possible the Klingons may have modified their genome during their period of experimentation with genetic engineering which ended during the Augment Wars. Though the Augment virus was reversed, it was not mentioned if other earlier modifications were affected.
The Klingon aging process is probably similar to Neanderthals. From paleontological evidence, it has been shown that a three year old Neanderthal child was as large, and as advanced physically, as a six year old Homo Sapien. It was not that they grew bigger as a species, but that they just reached adulthood much quicker.
Klingons likely mature in the same fashion. Given that they are a warrior race with a combative nature, it makes sense that they would need to reach adulthood relatively quickly.