The low carrier mobility of organic semiconductors and the high parasitic resistance and capacitance often encountered in conventional organic Schottky diodes hinder their deployment in emerging radio frequency (RF) electronics. Here, these limitations are overcome by combining self-aligned asymmetric nanogap electrodes (≈25 nm) produced by adhesion lithography, with a high mobility organic semiconductor, and RF Schottky diodes able to operate in the 5G frequency spectrum are demonstrated. C16IDT-BT is used, as the high hole mobility polymer, and the impact of p-doping on the diode performance is studied. Pristine C16IDT-BT-based diodes exhibit maximum intrinsic and extrinsic cutoff frequencies (fC) of >100 and 6 GHz, respectively. This extraordinary performance is attributed to the planar nature of the nanogap channel and the diode's small junction capacitance (<2 pF). Doping of C16IDT-BT with the molecular p-dopant C60F48 improves the diode's performance further by reducing the series resistance resulting to intrinsic and extrinsic fC of >100 and ≈14 GHz respectively, while the DC output voltage of an RF rectifier circuit increases by a tenfold. Our work highlights the importance of the planar nanogap architecture and paves the way for the use of organic Schottky diodes in large-area RF electronics of the future.