This article adopts a holistic approach to address the problem of poor broadband connectivity in rural areas by suggesting a novel wireless network architecture called "Frugal 5G Network." To arrive at the Frugal 5G Network architecture, we take into consideration 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 macrocells provide carpet coverage, while wireless local area networks (WLANs) provide additional capacity to serve village clusters. WLAN is backhauled via a wireless network also called the wireless middle mile network. We define software defined networking and network function virtualization 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). The proposed network architecture is developed independent of 3GPP 5G standards and can serve as a potential solution toward IEEE P2061, a standardization project that aims to design an architecture to facilitate rural broadband communication.