We prove congruences of Hecke eigenvalues between cuspidal Hilbert newforms \(f_{79}\) and \(h_{79}\) over \(F={{\mathbb {Q}}}(\sqrt{5})\) , of weights (2, 2) and (2, 4) respectively, level of norm 79. In the main example, the modulus is a divisor of 5 in some coefficient field, in the secondary example a divisor of 2. The former allows us to prove that the 4-dimensional mod-5 representation of \(\textrm{Gal}(\overline{{\mathbb {Q}}}/{{\mathbb {Q}}})\) on the \(3^{\textrm{rd}}\) cohomology of a certain Calabi-Yau threefold comes from a Siegel modular form \(F_{79}\) of genus 2, weight 3 and paramodular level 79. This is a weak form of a conjecture of Golyshev and van Straten. In aid of this, we prove also a congruence of Hecke eigenvalues between \(F_{79}\) and the Johnson-Leung-Roberts lift \(\textrm{JR}(h_{79})\) , which has weight 3 and paramodular level \(79\times 5^2\) .
