This article adopts a holistic approach to address the problem of poor broadband connectivity in rural areas by suggesting a novel wireless network architecture, also called the "Frugal 5G Network". To arrive at the Frugal 5G Network architecture, we take into consideration the rural connectivity needs and the characteristics specific to rural areas. As part of the proposed Frugal 5G Network, we define a heterogeneous Access Network wherein macro cells provide a carpet coverage while Wireless Local Area Networks (WLANs) provide additional capacity to serve the village clusters. WLAN is backhauled via a wireless network also called the wireless middle mile network. We define a Software Defined Networking (SDN) and Network Function Virtualization (NFV) based architecture to make the network flexible and scalable. The concepts of Fog computing have also been employed in the network architecture to bring intelligence to the edge, i.e., to the access network. Through a novel amalgamation of these technologies, we are able to address the connectivity requirements of rural areas. The proposed network architecture can serve as a potential solution towards IEEE P2061, a standardization project that aims to design an architecture to facilitate rural broadband communication.