A crucial yet challenging task in galaxy evolution studies is the identification of distant merging galaxies, a task that suffers from a variety of issues ranging from telescope sensitivities and limitations to the inherently chaotic morphologies of young galaxies. In this paper, we use random forests and convolutional neural networks to identify high-redshift JWST Cosmic Evolution Early Release Science Survey (CEERS) galaxy mergers. We train these algorithms on simulated 3 < z < 5 CEERS galaxies created from the IllustrisTNG subhalo morphologies and the Santa Cruz SAM light cone. We apply our models to observed CEERS galaxies at 3 < z < 5. We find that our models correctly classify ∼60%–70% of simulated merging and nonmerging galaxies; better performance on the merger class comes at the expense of misclassifying more nonmergers. We could achieve more accurate classifications, as well as test for a dependency on physical parameters such as gas fraction, mass ratio, and relative orbits, by curating larger training sets. When applied to real CEERS galaxies using visual classifications as ground truth, the random forests correctly classified 40%–60% of mergers and nonmergers at 3 < z < 4 but tended to classify most objects as nonmergers at 4 < z < 5 (misclassifying ∼70% of visually classified mergers). On the other hand, the CNNs tended to classify most objects as mergers across all redshifts (misclassifying 80%–90% of visually classified nonmergers). We investigate what features the models find most useful, as well as the characteristics of false positives and false negatives, and also calculate merger rates derived from the identifications made by the models.