Summary: For \(N \geq 5\) and \(a>0\), we consider the following semipositone problem \[ \Delta^2 u = g(x) f_a(u) \text{ in } \mathbb{R}^N, \text{ and } u \in \mathcal{D}^{2, 2}(\mathbb{R}^N), \qquad \quad \text{(SP)} \] where \(g \in L^1_{loc}(\mathbb{R}^N)\) is an indefinite weight function, \(f_a : \mathbb{R} \to \mathbb{R}\) is a continuous function that satisfies \(f_a(t) = -a\) for \(t \in \mathbb{R}^-\), and \(\mathcal{D}^{2, 2}(\mathbb{R}^N)\) is the completion of \(\mathcal{C}_c^{\infty}(\mathbb{R}^N)\) with respect to \((\int_{\mathbb{R}^N} (\Delta u)^2)^{1/2}\). For \(f_a\) satisfying subcritical nonlinearity and a weaker Ambrosetti-Rabinowitz type growth condition, we find the existence of \(a_1>0\) such that for each \(a \in (0, a_1)\), (SP) admits a mountain pass solution. Further, we show that the mountain pass solution is positive if \(a\) is near zero. For the positivity, we derive uniform regularity estimates of the solutions of (SP) for certain ranges in \((0, a_1)\), relying on the Riesz potential of the biharmonic operator.