Millimeter wave (mmWave) is a key band for fifth-generation (5G) mobile communication that features large available bandwidth and high data rates. Antenna elements are recommended to be dual-polarized, compact, wideband, and high gain to be utilized for 5G array antenna systems. In this paper, a miniaturized gain-enhanced Vivaldi antenna element in an evolutional-oriented process is designed, simulated, and successfully measured for 5G mmWave applications. The size of the antenna is as compact as 5.5mm x 12mm. The measured operational bandwidth of the antenna element is between 22.5 - 45 GHz covering 5G n257, n258, n259, n260, and n261 frequency bands even though the simulation results reveal the extension of the bandwidth to 70 GHz. The results show a nearly constant end-fire radiation pattern with a measured gain of more than 5dBi across the whole bandwidth. The comparison of the proposed antenna with the most recent related works justifies the novelties and advantages of the antenna in terms of 5G requirements, bandwidth, and compactness properties. The proposed antenna element is a suitable candidate for large antenna arrays and 5G MIMO applications.