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We present in this paper the results of high spectral resolution ($R$=88,100) spectroscopy at 4.7 $μ$m with iSHELL/IRTF of hot molecular gas close to the massive binary protostar W3 IRS5. The binary was spatially resolved and the spectra of the two sources (MIR1 and MIR2) were obtained simultaneously for the first time. Hundreds of $^{12}$CO $ν$=0-1, $ν$=1-2 lines, and $ν$=0-1 transitions of the isotopes of $^{12}$CO were detected in absorption, and are blue-shifted compared to the cloud velocity $v_{LSR}=-$38 km/s. We decompose and identify kinematic components from the velocity profiles, and apply rotation diagram and curve of growth analyses to determine their physical properties. Temperatures and column densities of the identified components range from 30$-$700 K and 10$^{21}-$10$^{22}$ cm$^{-2}$, respectively. Our curve of growth analyses consider two scenarios. One assumes a foreground slab with a partial covering factor, which well reproduces the absorption of most of the components. The other assumes a circumstellar disk with an outward decreasing temperature in the vertical direction, and reproduces the absorption of all the hot components. We attribute the physical origins of the identified components to the foreground envelope ($<$100 K), post-J-shock regions (200$-$300 K), and clumpy structures on the circumstellar disks ($\sim$600 K). We propose that the components with a J-shock origin are akin to water maser spots in the same region, and are complementing the physical information of water masers along the direction of their movements.