ApJ, 950, 58 (2023) We report the discovery of five bright strong gravitationally lensed galaxies at $3 < z < 4$: COOLJ0101$+$2055 ($z = 3.459$), COOLJ0104$-$0757 ($z = 3.480$), COOLJ0145$+$1018 ($z = 3.310$), COOLJ0516$-$2208 ($z = 3.549$), and COOLJ1356$+$0339 ($z = 3.753$). These galaxies have magnitudes of $r_{\rm AB}, z_{\rm AB} < 21.81$ mag and are lensed by galaxy clusters at $0.26 < z < 1$. This sample nearly doubles the number of known bright lensed galaxies with extended arcs at $3 < z < 4$. We characterize the lensed galaxies using ground-based grz/giy imaging and optical spectroscopy. We report model-based magnitudes and derive stellar masses, dust content, and star-formation rates via stellar population synthesis modeling. Building lens models based on ground-based imaging, we estimate source magnifications in the range $\sim$29 to $\sim$180. Combining these analyses, we derive demagnified stellar masses in the range $\rm log_{10}(M_{*}/M_{\odot}) \sim 9.69 - 10.75$ and star formation rates in the youngest age bin ranging from $\rm log_{10}(SFR/(M_{\odot}\cdot yr^{-1})) \sim 0.39 - 1.46$, placing the sample galaxies on the massive end of the star-forming main sequence in this redshift interval. In addition, three of the five galaxies have strong Ly$\alpha$ emissions, offering unique opportunities to study Ly$\alpha$ emitters at high redshift in future work.