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Weren't Europeans of that era smaller on average than today's?
Yes, but 5'8" or 5'9" was quite common--5'5" was still kind of short. Author James Jones once noted that in a World War Two American outfit, a six-foot tall man would always be nicknamed "Stretch" for his unusual size. The 1950's began the era of vitamin-fortified everything, and the Baby Boomers were generally taller than their parents.
For the generation that matured in the 1930's, not only were diets generally vitamin-poor during the winter months, but the deprivation of the Great Depression era meant that diets for millions of people were starchy and vitamin-poor year-round.