This paper presents a single-fed, single-layer, dual-band antenna with a large frequency ratio of 4.74:1 for vehicle-to-vehicle communication. The antenna consists of a 28 GHz inset-fed rectangular patch embedded into a 5.9 GHz patch antenna for dual-band operation. The designed dual-band antenna operates from 5.81 to 5.99 GHz (Dedicated Short Range Communications, DSRC) and 27.9 to 30.1 GHz (5G millimeter-wave (mm-wave) band). Furthermore, the upper band patch was modified by inserting slots near the inset feed line to achieve an instantaneous bandwidth of 4.5 GHz. The antenna was fabricated and measured. The manufactured prototype operates simultaneously from 5.8 to 6.05 GHz and from 26.8 to 31.3 GHz. Notably, the designed dual-band antenna offers a high peak gain of 7.7 dBi in the DSRC band and 6.38 dBi in the 5G mm-wave band.