Let \(p\) be \(1\) or a prime number. Let \(\Gamma_0^+(p)\) be the Fricke group generated by the Hecke group \(\Gamma_0(p)\) and the Fricke involution. Let \(M_k^!(\Gamma_0^+(p))\) be the space of weakly holomorphic modular forms of even weight \(k\). This space has a natural basis \(\{f_{k,m}\}_{m\ge m_{p,k}}\) such that \(f_{k,m}(z)=q^{-m}+O(q^{m_{p,k}+1})\), where \(m_{p,k}\) is a uniquely determined positive integer by \(p\) and \(k\), and \(q=e^{2\pi i z}\). The problem here is concerned with the location of zeros of the forms \(f_{k,m}\). In the case where \(p=1,2\) and \(3\), this problem is solved by \textit{W. Duke} and \textit{P. Jenkins} [Pure Appl. Math. Q. 4, No. 4, 1327--1340 (2008; Zbl 1200.11027)], \textit{S. Choi} and \textit{B.-H. Im} [J. Number Theory 166, 298--323 (2016; Zbl 1417.11029)], \textit{S. Hanamoto} and the author [Acta Arith. 197, No. 1, 37--54 (2021; Zbl 1465.11115)], respectively. In this article, the author deals with the cases where \(p=5\) and \(7\). To state his result let us consider a fundamental domain \(F^+(p)\) of \(\Gamma_0^+(p)\) containing arcs \(\{z~|~|z|=1/\sqrt p,|z+1/2|=1/2\sqrt p,-1/2\le\mathrm{Re}(z)\le 0 \}\) as lower boundaries. The main result is that all the zeros in \(F^+(p)\) of \(f_{k,m}\) lie on the lower boundary arcs for sufficiently large \(m\). The principal idea of proof is based on previous works for \(p\le 3\) but requires more fine estimations.