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We present Herschel observations of the water molecule in the massive star-forming region W3 IRS5. The o-H₂¹⁷O 1₁₀-1₀₁, p-H₂¹⁸O 1₁₁-0₀₀, p-H₂O 2₀₂-1₁₁, p-H₂O 1₁₁-0₀₀, o-H₂O 2₂₁-2₁₂, and o-H₂O 2₁₂-1₀₁ lines, covering a frequency range from 552 up to 1669GHz, have been detected at high spectral resolution with HIFI. The water lines in W3 IRS5 show well-defined high-velocity wings that indicate a clear contribution by outflows. Moreover, the systematically blue-shifted absorption in the H₂O lines suggests expansion, presumably driven by the outflow. No infall signatures are detected. The p-H₂O 1₁₁-0₀₀ and o-H₂O 2₁₂-1₀₁ lines show absorption from the cold material (T∼10K) in which the high-mass protostellar envelope is embedded. One-dimensional radiative transfer models are used to estimate water abundances and to further study the kinematics of the region. We show that the emission in the rare isotopologues comes directly from the inner parts of the envelope (T > 100 K) where water ices in the dust mantles evaporate and the gas-phase abundance increases. The resulting jump in the water abundance (with a constant inner abundance of 10^–4) is needed to reproduce the o-H₂¹⁷O 1₁₀-1₀₁ and p-H₂¹⁸O 1₁₁-0₀₀ spectra in our models. We estimate water abundances of 10^–8 to 10^–9 in the outer parts of the envelope (T≲100K). The possibility of two protostellar objects contributing to the emission is discussed.