Résumé
We give here some new lower bounds on the order of a largest induced forest in planar graphs with girth$4$and$5$ . In particular we prove that a triangle-free planar graph of order$n$admits an induced forest of order at least$\frac{6n+7}{11}$, improving the lower bound of Salavatipour [M. R. Salavatipour, Large induced forests in triangle-free planar graphs, Graphs and Combinatorics, 22:113-126, 2006]. We also prove that a planar graph of order$n$and girth at least$5$admits an induced forest of order at least$\frac{44n+50}{69}$ .