We present statistical analysis of 16,903 current sheets (CSs) observed over 641 days aboard Ulysses spacecraft at 5 AU. We show that the magnetic field rotates across CSs through some shear angle, while only weakly varies in magnitude. The CSs are typically asymmetric with statistically different, though only by a few percent, magnetic field magnitudes at the CS boundaries. The data set is classified into about 90.6% non‐bifurcated and 9.4% bifurcated CSs. Most of the CSs are proton kinetic‐scale structures with the half‐thickness of non‐bifurcated and bifurcated CSs within respectively 200–2,000 km and 500–5,000 km or 0.5–5λp and 0.7–15λp in units of local proton inertial length. The amplitude of the current density, mostly parallel to magnetic field, is typically within 0.05–0.5 nA/m2 or 0.04–0.4JA in units of local Alfvén current density. The CSs demonstrate approximate scale‐invariance with the shear angle and current density amplitude scaling with the half‐thickness, Δθ≈16.6°λ/λp0.34 ${\Delta }\theta \approx 16.6{}^{\circ}\,{\left(\lambda /{\lambda }_{p}\right)}^{0.34}$ and J0/JA≈0.14λ/λp−0.66 ${J}_{0}/{J}_{A}\approx 0.14\,{\left(\lambda /{\lambda }_{p}\right)}^{-0.66}$. The matching of the magnetic field rotation and compressibility observed within the CSs against those in ambient solar wind indicate that the CSs are produced by turbulence, inheriting its scale‐invariance and compressibility. The estimated asymmetry in plasma beta between the CS boundaries is shown to be insufficient to suppress magnetic reconnection through the diamagnetic drift of X‐line. The presented results will be of value for future comparative analysis of CSs observed at different distances from the Sun. Plain Language Summary Current sheets (CSs) are coherent structures potentially contributing to solar wind heating and particle acceleration. These structures are highly‐likely produced by turbulence, but the alternative hypothesis of coronal origin has not been ruled out. The analysis of CSs at different distances from the Sun may potentially shed light onto the origin and contribution of these structures to solar wind heating and particle acceleration. While there are comprehensive analyses of solar wind CSs at 1 AU and near the Sun, there is still no equivalent analysis of these structures well beyond 1 AU. In this study we present an extensive statistical study of CSs observed aboard Ulysses around 5 AU. We demonstrate that the CSs are predominantly rotations of the magnetic field, typically occurring on proton kinetic scales and exhibiting approximate scale‐invariance. We provide strong evidence that the CSs are produced by turbulence and inherit the scale‐invariance and magnetic field compressibility typical of turbulence. The presented results will be valuable for understanding solar wind turbulence, solar wind heating and particle acceleration at different distances from the Sun. Key Points Current sheets (CSs) are predominantly rotations of the magnetic field on proton kinetic scales Scale‐invariant properties strongly indicate that CSs are produced by turbulence The asymmetry of CSs is typically insufficient to suppress magnetic reconnection