Methyl-5-uridine (m5U) is one the most abundant non-canonical bases present in cellular RNA, and in yeast is found at position U54 of tRNAs where modification is catalysed by the methyltransferase Trm2. Although the mammalian enzymes that catalyse m5U formation are yet to be identified via experimental evidence, based on sequence homology to Trm2, two candidates currently exist, TRMT2A and TRMT2B. Here we developed a genome-wide single-nucleotide resolution mapping method, Fluorouracil-Induced-Catalytic-Crosslinking-Sequencing (FICC-Seq), in order to identify the relevant enzymatic targets. We demonstrate that TRMT2A is responsible for the majority of m5U present in human RNA, and that it commonly targets U54 of cytosolic tRNAs. By comparison to current methods, we show that FICC-Seq is a particularly robust method for accurate and reliable detection of relevant enzymatic target sites. Our associated finding of extensive irreversible TRMT2A-tRNA crosslinking in vivo following 5-Fluorouracil exposure is also intriguing, as it suggests a tangible mechanism for a previously suspected RNA-dependent route of Fluorouracil-mediated cytotoxicity.