Short cycles of low weight in normal plane maps with minimum degree 5

In this note, precise upper bounds are determined for the minimum degree-sum of the vertices of a 4-cycle and a 5-cycle in a plane triangulation with minimum degree 5: w(C₄) ≤ 25 and w(C₅) ≤ 30. These hold because a normal plane map with minimum degree 5 must contain a 4-star with ${\displaystyle w\left(K_{1,4}\right)\le 30}$. These results answer a question posed by Kotzig in 1979 and recent questions of Jendrol' and Madaras.