A dual-polarized symmetrically cross-slotted square patch (SCSSP) antenna with multimode resonance is proposed for 5G millimeter-wave broadband applications. A symmetrical cross-slot is etched on the square patch surface to change the original E-field distribution where a whole square patch is cut into four disconnected equal parts. For both polarizations, this etching also tunes the resonance frequencies of the two modes to be sufficiently close to each other. Therefore, the antenna can realize good impedance performance within the wide designated bandwidth. Dual-polarized radiation of the SCSSP is vertically excited by three bow-tie-shaped slots and fed by two orthogonal substrate integrated coaxial lines. Simulated and measured results show that the fabricated prototype achieves a broad overlapped impedance bandwidth of 50.0% (24-40 GHz), isolation higher than 30 dB between the two input ports, stable radiation pattern, and low cross-polarization over the operating band. Moreover, the proposed SCSSP antenna with compact size, planar shape, and simple vertical feeding is very well-suited for two-dimensional array design.