Interferon (IFN) responses play key roles in cellular defense against pathogens. Highly expressed IFN-induced proteins with tetratricopeptide repeats (IFITs) are proposed to function as RNA binding proteins, but the RNA binding and discrimination specificities of IFIT proteins remain unclear. Here we show that human IFIT5 has comparable affinity for RNAs with diverse phosphate-containing 5'-ends, excluding the higher eukaryotic mRNA cap. Systematic mutagenesis revealed that sequence substitutions in IFIT5 can alternatively expand or introduce bias in protein binding to RNAs with 5' monophosphate, triphosphate, cap0 (triphosphate-bridged N7-methylguanosine), or cap1 (cap0 with RNA 2'-O-methylation). We defined the breadth of cellular ligands for IFIT5 by using a thermostable group II intron reverse transcriptase for RNA sequencing. We show that IFIT5 binds precursor and processed tRNAs, as well as other RNA polymerase III transcripts. Our findings establish the RNA recognition specificity of the human innate immune response protein IFIT5