When I was in 7th grade, I won my school's spelling bee, and the resource teacher who ran the bee brought me to her office to call my parents and to get me signed up for the county-wide spelling bee. She was *astounded* that my SS number was so similar to hers. They both started with the same first 5 numbers. Well, the first 3 are for what area your card was assigned in (or, at least, they used to be, no idea if this has changed). I have no idea what the middle two numbers are, but a lot of people I know have the same middle numbers, even if all numbers are different. So, yes, we had 5 digits alike, but it wasn't exactly a shock that we would do so, apparently both being born in the same geographical area, which we still lived in. The last 4 were completely different.
Of course, my mother and brother have SS numbers that are only a few digits apart, despite being born decades apart!