The fifth generation (5G) of wireless communication networks represents a groundbreaking shift in the realm of connectivity, enabling a wide array of transformative applications and services. This article delves into the pivotal role played by modulation and coding methods in the context of 5G networks. It explores their significance, delves into recent research and publications within the field, and outlines the direction for future research endeavors. Modulation and coding (M&C) are fundamental for 5G networks, enhancing data rates, reliability, and reducing interference. This article delves into their role in 5G networks, addressing challenges, including fading channels, interference, and diverse user needs. Recent research explores advanced modulation schemes like 256-QAM and 1024-QAM, requiring error correction coding techniques like Turbo codes and LDPC codes. Massive MIMO, using multiple antennas at both ends, is supported by adaptive coding and modulation. Adaptive Modulation and Coding (AMC) dynamically adjusts schemes based on real-time channel conditions, balancing data rate and reliability. Non-Orthogonal Multiple Access (NOMA) accommodates massive device connectivity, allowing multiple users to share resources with different power levels and modulation schemes. The study aims to comprehensively analyze 5G's M&C methods, assess modulation schemes for higher data rates, evaluate error correction coding, investigate Massive MIMO and adaptive modulation for spectral efficiency, and scrutinize NOMA's potential for massive device connectivity. Results highlight the importance of advanced modulation schemes, efficient error correction coding, and adaptive techniques in realizing 5G objectives, enabling higher data rates, lower latency, and improved reliability. NOMA is promising for accommodating many connected devices in 5G. M&C are essential for efficient and reliable data transmission in 5G, with ongoing research refining techniques for 6G and beyond. Integrating machine learning and AI into M&C algorithms holds promise for enhancing network efficiency and reliability.