Summary: A feedback vertex set of a graph is a subset of vertices intersecting all cycles. We provide tight upper bounds on the size of a minimum feedback vertex set in planar graphs of girth at least five. We prove that if \(G\) is a connected planar graph of girth at least five on \(n\) vertices and \(m\) edges, then \(G\) has a feedback vertex set of size at most \(\frac{2m-n+2}{7}\). By Euler’s formula, this implies that \(G\) has a feedback vertex set of size at most \(\frac{m}{5}\) and \(\frac{n-2}{3}\). These results not only improve a result of F. Dross et al. [Discrete Appl. Math. 214, 99–107 (2016; Zbl 1346.05039)] and confirm the girth-5 case of one of their conjectures, but also make the best known progress towards a conjecture of L. Kowalik et al. [Discrete Math. Theor. Comput. Sci. 12, No. 1, 87–100 (2010; Zbl 1250.05041)] and solve the subcubic case of their conjecture. An important step of our proof is providing an upper bound on the size of minimum feedback vertex sets of subcubic graphs with girth at least five with no induced subdivision of members of a finite family of non-planar graphs.