It is important to remember that "life expectancy" is almost exclusively the average age of a population at death, meaning that a high number of early deaths among infants and children drag the average life expectancy down. In Classical Rome, a third of babies died before their first birthday, and half of children died before their tenth, according to Karen Cokayn. If someone survived past ten years old, they could expect to live until they were fifty or sixty, with some happily living until their eighties, an age we would consider elderly in an advanced, modern, country.

Essentially, describing Jesus as elderly at the time of his crucifixion would be inconsistent with the historical reality that, provided you survived childhood (no easy feat in itself, to be fair), it was more than possible to continue living for decades to come.

Source: Karen Cokayn, Experiencing Old Age in Ancient Rome, page 2-3

I'm not an expert in this field, but I believe that while life expectancy has increased much of that has been because of lowered infant mortality. People who lived into adulthood would be likely to make old age.

“So someone at 35 wouldn't have been seen as an "old person." "From around the first century B.C. onwards, the age of 60 or 65 was commonly mentioned as the threshold of old age," writes Karen Cokayne in "Experiencing Old Age in Ancient Rome." That's also when you got out of previous public obligations, like jury duty (yay!).”

http://www.revealedrome.com/2012/06/ancient-rome-daily-life-women-age.html

I would like to add to the previous responses that life expectancy, at the time, depended heavily on social class. If you were poor or a farmer, and you made it past childhood, you could expect to die anywhere between the ages of 20 and 40, while the rich could expect to live into their 60's and 70's, or beyond.