Fluid antenna system (FAS) is an emerging technology that uses the new form of shape- and position-reconfigurable antennas to empower the physical layer for wireless communications. Prior studies on FAS were however limited to narrowband channels. Motivated by this, this paper addresses the integration of FAS in the fifth generation (5G) orthogonal frequency division multiplexing (OFDM) framework to address the challenges posed by wideband communications. We propose the framework of the wideband FAS OFDM system that includes a novel port selection matrix. Then we derive the achievable rate expression and design the adaptive modulation and coding (AMC) scheme based on the rate. Extensive link-level simulation results demonstrate striking improvements of FAS in the wideband channels, underscoring the potential of FAS in future wireless communications.