You seem to be using a very broad definition of 'science'. What do you mean by the term? Do we know mathematical truths via science, or is that a different realm of knowledge? Are philosophical arguments categorizable as science? What about questions that are in theory testable, but the test involves huge numbers of complex interfering factors and decades of time (like many questions of political and social policy) - are they usefully labeled as scientific questions, or do we gain something by recognizing them as requiring some other mode of knowledge than just empirical observations?

> answerable questions not addressable by science

So what does 'answerable' mean? There's no such thing as proof, rigorously speaking, outside of math and other formal systems, and not always within them. The answers that the best hard science provides are strong, but not provably certain, and the spectrum of certainty extends a long way down from there - at what level of certainty does an answer stop being an answer? I think there are many important questions that don't admit hard scientific answers, and for which 'science' as I understand the term isn't the most useful mode of knowledge for finding the 'answers' that are most likely to be fruitful.