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We give here some new lower bounds on the order of a largest induced forestin planar graphs with girth $4$ and $5$. In particular we prove that atriangle-free planar graph of order $n$ admits an induced forest of order atleast $\frac{6n+7}{11}$ , improving the lower bound of Salavatipour [M. R.Salavatipour, Large induced forests in triangle-free planar graphs, Graphs andCombinatorics, 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$\frac{44n+50}{69}$.

Large induced forests in planar graphs with girth 4 or 5