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We present an analysis of X-ray high-quality grating spectra of the Seyfert 1 galaxy NGC 5548 using archival Chandra-High Energy Transmission Grating Spectrometer and Low Energy Transmission Grating Spectrometer observations for a total exposure time of 800 ks. The continuum emission (between 0.2 keV and 8 keV) is well represented by a power law (Γ = 1.6) plus a blackbody component (kT = 0.1 keV). We find that the well-known X-ray warm absorber (WA) in this source consists of two different outflow velocity systems. One absorbing system has a velocity of -1110±150 km/s and the other of -490±150 km/s. Recognizing the presence of these kinematically distinct components allows each system to be fitted independently, each with two absorption components with different ionization levels. The high-velocity system consists of two components, one with a temperature of 2.7±0.6x10⁶ K, log U = 1.23, and another with a temperature of 5.8±1.0x10⁵ K, log U = 0.67. The high-velocity, high-ionization component produces absorption by charge states Fe XXI-XXIV, while the high-velocity, low-ionization component produces absorption by Ne IX-X, Fe XVII-XX, and O VII-VIII. The low-velocity system also required two absorbing components, one with a temperature of 5.8±0.8 x10⁵ K, log U = 0.67, producing absorption by Ne IX-X, Fe XVII-XX, and O VII-VIII, and the other with a lower temperature of 3.5±0.35x10⁴ K and a lower ionization of log U = -0.49, producing absorption by O VI-VII and the Fe VII-XII M-shell Unresolved Transitions Array. Once these components are considered, the data do not require any further absorbers. In particular, a model consisting of a continuous radial range of ionization structures (as suggested by a previous analysis) is not required. The two absorbing components in each velocity system are in pressure equilibrium with each other. This suggests that each velocity system consists of a multi-phase medium. This is the first time that different outflow velocity systems have been modeled independently in the X-ray band for this source. The kinematic components and column densities found from the X-rays are in agreement with the main kinematic components found in the UV absorber. This supports the idea that the UV and X-ray absorbing gas is part of the same phenomenon. NGC 5548 can now be seen to fit in a pattern established for other WAs: two or three discrete phases in pressure equilibrium. There are no remaining cases of a well-studied WA in which a model consisting of a multi-phase medium is not viable.