Well, yes. As near as I can tell, 80% of my mother's family are diabetic, including three of her four boys (and the 4th is seemingly borderline). Her mother, grandmother, both brothers, all of her maternal uncles. There are a couple of my great-aunts that aren't, but that's it. My mother is technically Pre-Diabetic, but she's also 70, so hard to say whether it's the persistent LADA that runs in the family or just age. So pretty much my entire family on Mom's side. Dad's side is seemingly impervious to everything: no cancer, no heart disease, no diabetes. They do get high cholesterol (which I inherited), but it never seems to cause heart attacks or strokes.
As for the science behind it, all forms of diabetes (other than physically-caused diabetes from a pancrectomy or similar) are, so far as we know, genetic in basis. There are two ways this works: there are genetic mutations in MODY and MIDD (both very rare) that directly cause beta cell dysfunction to various degree; to develop Type 1 or 2, it is necessary to first have certain (widely varying) genetic sequences. Type 1 is then kicked off by an environmental event that primes the immune system to attack beta cells or insulin itself (or both and then some). Type 2 is cryptic, in the sense that the mechanism is poorly understood, but it doesn't seem possible to "eat your way into it" if you don't have the genetic sequences. And it definitely runs in families and populations.
So, although it certainly seems high, 5/6 kids developing diabetes doesn't seem a statistical outlier. What type of DM do you and your siblings have, if you don't mind my asking?