We present a search for associated production of Higgs and $W$ bosons in $p\bar{p}$ collisions at a center of mass energy of $\sqrt{s}=1.96$ TeV in 5.3 fb$^{-1}$ of integrated luminosity recorded by the D0 experiment. Multivariate analysis techniques are applied to events containing one lepton, an imbalance in transverse energy, and one or two $b$-tagged jets to discriminate a potential $WH$ signal from standard model backgrounds. We observe good agreement between data and background, and set an upper limit of 4.5(at 95% confidence level and for $m_H=115$ GeV) on the ratio of the $WH$ cross section multiplied by the branching fraction of $H \rightarrow b \bar{b}$ to its standard model prediction. A limit of 4.8 is expected from simulation.