In this paper, we investigate a transitioning model of Bianchi type V universe in Brans-Dicke theory of gravitation. The derived model not only validates Machs principle but also describes the present acceleration of the universe. In this paper, our aim is to constrain an exact Bianchi type V universe in Brans - Dicke gravity. For this sake, firstly we obtain an exact solution of field equations in modified gravity and secondly constrain the model parameters by bounding the model with recent $H(z)$ and Baryon acoustic oscillations (BAO) observational data. The current phase of accelerated expansion of the universe is also described by the contribution coming from cosmological constant screened scalar field with deceleration parameter showing a transition redshift of about $z_{t} = 0.79$. Some physical properties of the universe are also discussed.
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