In this talk I will give an introduction to the modular approach to Fermat-type equations via Hilbert cuspforms and discuss how it can be used to show that certain equations of the form $x^{13}+y^{13}=C{z}^p$ have no solutions $(a,b,c)$ such that $\gcd (a,b)=1$ and $13\nmid c$ if $p>4992539$. We will first relate a putative solution of the previous equation to the solution of another Diophantine equation with coefficients in $Q(\sqrt{13})$. Then we attach Frey curves $E$ over $Q(\sqrt{13})$ to solutions of the latter equation. Finally, we will discuss on the modularity of $E$ and irreducibility of certain Galois representations attached to it. These ingredients enable us to apply a modular approach via Hilbert newforms to get the desired arithmetic result on the equation.