Fluid antenna multiple access (FAMA), enabled by the fluid antenna system (FAS), offers a new and straightforward solution to massive connectivity. Previous results on FAMA were primarily based on narrowband channels. This paper studies the adoption of FAMA within the fifth-generation (5G) orthogonal frequency division multiplexing (OFDM) framework, referred to as OFDM-FAMA, and evaluate its performance in broadband multipath channels. We first design the OFDM-FAMA system, taking into account 5G channel coding and OFDM modulation. Then the system's achievable rate is analyzed, and an algorithm to approximate the FAS configuration at each user is proposed based on the rate. Extensive link-level simulation results reveal that OFDM-FAMA can significantly improve the multiplexing gain over the OFDM system with fixed-position antenna (FPA) users, especially when robust channel coding is applied and the number of radio-frequency (RF) chains at each user is small.