Media applications are amongst the most demanding services in terms of resources, requiring huge network capacity for high bandwidth audio-visual and other mobile sensory streams. The 5G-MEDIA project aims at innovating media-related applications by investigating how these applications and the underlying 5G network should be coupled and interwork to the benefit of both. The 5G-MEDIA approach aims at delivering an integrated programmable service platform for the development, design and operations of media applications in 5G networks by providing mechanisms to flexibly adapt service operations to dynamic conditions and react upon events (e.g. to transparently accommodate auto-scaling of resources, VNF replacement, etc.). In this paper we present the 5G-MEDIA service platform architecture, which has been specifically designed to enable the development and operation of services for the nascent 5G media industry. Our approach delivers an integrated programmable service platform for the development, design and operations of media applications in 5G networks.