Universal Filtered Multi-Carrier (UFMC) is a promising waveform for 5G and beyond wireless systems due to its superior spectral localization and low-latency characteristics; however, its high Peak-to-Average Power Ratio (PAPR) significantly degrades power amplifier efficiency and causes nonlinear distortion and out-of-band (OOB) emissions. To address these limitations, this paper proposes an Adaptive Hybrid Orthogonal Precoding with Gaussianized Companding (AHO-PCG) framework for PAPR-aware UFMC transmission. The proposed approach integrates adaptive orthogonal precoding, Gaussianized Dynamic Companding (GDC), and Selective Subcarrier Companding (SSC) within a joint optimization loop to balance PAPR reduction, signal fidelity, and spectral containment. Gaussianization reshapes the signal amplitude distribution to suppress extreme peaks, while adaptive precoding dynamically selects suitable orthogonal transforms based on signal characteristics, and SSC limits nonlinear processing to dominant peak-contributing subcarriers. Simulation results under 3GPP LTE-compliant parameters using QPSK, 16-PSK, and 64-QAM demonstrate that AHO-PCG achieves up to 4.4 dB PAPR reduction at a CCDF of 10⁻³, reduces EVM to 2.9%, suppresses OOB emissions to –42 dBm, and improves BER by up to an order of magnitude compared to baseline UFMC. These gains are achieved with a modest processing overhead, making the framework suitable for real-time 5G baseband implementations and extensible to future 6G waveform designs.