The provision of both wireless and wired services in the optical access domain will be an important function for future passive optical networks (PON). With the emergence of 5th generation (5G) mobile communications, a move toward a dense deployment of small cell antenna sites, in conjunction with a cloud radio access network (C-RAN) architecture, is foreseen. This type of network architecture greatly increases the requirement for high capacity mobile fronthaul and backhaul links. An efficient way of achieving such connectivity is to make use of wavelength division multiplexed (WDM) PON infrastructure where wireless and wired services may be converged for distribution. In this work, for the first time, the convergence of 5G wireless candidate waveforms with a single-carrier wired signal is demonstrated in a PON. Three bands of universally filtered orthogonal frequency division multiplexing (UF-OFDM) and generalized frequency division multiplexing (GFDM), are transmitted at an intermediate frequency in conjunction with a digital 10Gb/s pulse amplitude modulation (PAM-4) signal in the downlink direction. Orthogonal frequency division multiplexing (OFDM) is also evaluated as a benchmark. Results show, for each waveform, how performance varies due to the 5G channel spacing - indicating UF-OFDM's superiority in terms of PON convergence. Successful transmission over 25km of fibre is also demonstrated for all waveforms.