We present the 0.5–50 keV Suzaku broad-band X-ray spectral study of the Compton-thick active galactic nucleus (AGN) in NGC 5135. The Suzaku observation provides the first detection of NGC 5135 above 10 keV that allowed us, for the first time, to estimate the absorbing column density, the intrinsic X-ray luminosity, the strength of the reflection component and the viewing angle of the torus for this AGN. The 0.5–10 keV spectrum of NGC 5135 is characterized by the standard components for a Compton-thick source: a scattered continuum, a prominent Fe Kα emission line [equivalent width (EW) ∼ 2.1 keV] and a soft excess. At higher energies (E > 10 keV), the intrinsic AGN continuum shows up, implying an absorbing column density of the order of ∼2.5 × 1024 cm−2 and the intrinsic 2.0–10 keV X-ray luminosity of ∼1.8 × 1043 erg s−1. Assuming a toroidal geometry of the reprocessing material, we show that an edge-on view of the obscuring torus is preferred in this source.