Wilson loop amplitudes are a central concept in gauge theories, offering a way to study the behavior of particles and their interactions with gauge fields as they move along closed paths in spacetime. In this talk, we give a mathematical description of Wilson loop amplitudes in 5D gauge theory. This description will lead to conjectures about structures of Gromov-Witten invariants of some compact semi-Fano (not Calabi-Yau) threefolds. We will give some evidence for these conjectures. This is a work in progress with Shuai Guo and Xin Wang.