The frightening growth of bacterial infections and their resistance to most first-line antibiotic drugs have made antibacterial therapy challenging. High accuracy, reduced time and effort, high cost, and a theoretical chemical study to find alternative treatments are preferable considerations. Chemical programs designed 150 fluoroquinolones in a theoretical study, and determined the top five based on their optimal binding affinity. The binding affinity (G) was calculated in Swiss Dock; a more negative G indicates a more suitable binding between the compound and the protein. This study selected the top five fluoroquinolones against each protein. The ΔG calculations indicate compound B has the highest inhibitory activity against Staphylococcus aureus (ΔG= -7.562 kcal/mol). Compound C has the strongest inhibitory activity against E. coli (ΔG= -8.562 kcal/mol) because it interacts with the Gyrase B protein. Compound A has the strongest inhibitory activity against Streptococcus pyogenes (ΔG= -6.762 kcal/mol) because it interacts with the cysteine protease Spe B. Compound D has the strongest inhibitory activity against Klebsiella pneumoniae (ΔG= -7.524 kcal/mol) because it interacts with the NDM-1 protein (ΔG= -6.999 kcal/mol) through their interaction with the azobenzene reductase protein. The HOMO-LUMO energy gaps of compounds (A-E) were theoretically estimated at B3LYP in conjunction with the base 6-311G (d, p) using DFT-based structural optimization. Compound E (∆E Gap= 0.130 eV) is the one with the lowest energy gap. Compound C (∆E Gap= 0.1609 eV) is the one that has the largest energy gap.