It's a claim that's repeated at many web sites (if I take for granted that "average life expectancy is about 75 years").
For example the first few results found by searching for "amish life expectancy" on google include the following.
Researchers Study the Genetics of Longevity
in the Old Order Amish (from gerontology.umaryland.edu)
The current life expectancy of members
of the Old Order Amish community is
about 72 years, nearly the same as the life
expectancy of the average American.
Nearly, that is, except for two significant
differences. First, among the Amish, the
72-year life expectancy is for men and
women, while in the general population
women tend to outlive men by about
seven years. Second, the Amish have had
a 72-year life expectancy not only for the
past few decades, as have most
Americans, but for the last
300 years—since they settled in the
United States in the 1700s, when most
people living in America were dying in
THE AMISH OBESITY STUDIES
What makes the Amish such fertile ground for study on subjects such as weight loss is because they all live the same way they lived 300 years ago. They still plow their fields with horses, don't drive cars, use lanterns for electricity and only use telephones in a dire emergency. Their life expectancy is right at the US average even though they avoid modern medicine whenever they can...but the life expectancy of the Amish has been 72 or greater for almost 300 years, even when ours was 40 and they still eat like our ancestors did too, which is pretty much whatever they want. We don't recommend the Amish Diet, but there is much to be learned from the studies that measure their physical activity.
Heritability of life span in the Old Order Amish. (from ncbi.nlm.nih.gov)
Analyses were conducted on 1,655 individuals, representing all those born prior to 1890 and appearing in the most widely available genealogy, surviving until at least age 30 years, and with known date of death. Mean age at death (+/-SD) in this population was 70.7 +/- 15.6 years, and this did not change appreciably over time.
In summary it's very similar, or perhaps less by fewer than 10 years.