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This research proposes compact linearly polarized 5G Vivaldi non-uniform slot filtering antennas (VNSFAs) with stable radiation patterns and improved bandwidth (BW) and gain. The 5G third-order uniform transmission line hairpin bandpass filter (UTL HPBF) is first designed, and a 17.17 % size reduction is obtained using the non-uniform transmission line (NTL) theory. Secondly, the Vivaldi non-uniform slot profile antenna (VNSPA) theory is applied to design the UWB compact VNSA with 51.94 % size reduction, 2.91 %, and 5.8 % BW and gain enhancement. Finally, the predesigned compact UWB VNSA’s good performance is exploited in this work to be integrated with the compact 5G UTL and NTL HPBFs using a co-design methodology resulting in novel compact 6.55 GHz VNSFAs. These VNSFAs are compatible with modern wireless system miniaturization requirements. They are also considered good candidates for cognitive radio networks (CRNs) to mitigate spectrum scarcity. In this work, simulations are carried out using computer simulation technology (CST) software and they are validated by comparing them to the measured results. VNSFAs using UTL and NTL HPBFs provide measured S11 of <−10.35 dB and <−10.34 dB at 5.6–7.76 GHz and 6–7.76 GHz with peak realized gains of 4.84 dBi and 5.23 dBi, respectively. The obtained findings prove the effectiveness of using the simple and low-cost compactness techniques of NTL and VNSPA theories in reducing the filtenna size without degrading its performance.