Explaining SAT to high school science teachers
The permanent is #P-complete, even when restricted to $\{0,1\}$-valued matrices. The permanent can be used to compute certain parameters in statistical mechanics, see for example this paper on the dimer covering problem. Since I'm not a physicist, I cannot comment on whether these theoretical statistical mechanics problems are really useful; I suspect that they are not directly useful, but the area itself could lead to useful insights. It could also be the case that some of these parameters are useful on their own, but you'll have to consult with an expert.
Your 5 minute pitch could go something like this:

Statistical mechanics is a beautiful and deep part of physics and chemistry which studies how the emergent behavior of large systems results from microscopic physical laws operating on individual elements. It explains phenomena such as the laws of gasses, magnetization, and transitions between different phases of matter. Statistical mechanics is intimately connected to probability theory, computer science, operations research, and data science.
Many important quantities in statistical mechanics can be formulated as instances of #SAT. An algorithm for solving #SAT exactly or approximately can thus be used to predict physical and chemical phenomena.

This might somewhat overstate the case, but that's how sales pitches go.