The rotation state of small asteroids is affected in the long term by perturbing torques of gravitational and radiative origin (the YORP effect). Direct observational evidence of the YORP effect is the primary goal of our work. We carried out photometric observations of five near-Earth asteroids: (1862) Apollo, (2100) Ra-Shalom, (85989) 1999 JD6, (138852) 2000 WN10, and (161989) Cacus. Then we applied the light-curve inversion method to all available data to determine the spin state and a convex shape model for each of the five studied asteroids. In the case of (2100) Ra-Shalom, the analysis required that the spin-axis precession due to the solar gravitational torque also be included. We obtained two new detections of the YORP effect: (i) $(2.9 \pm 2.0)\times 10^{-9}\,\mathrm{rad\,d}^{-2}$ for (2100) Ra-Shalom, and (ii) $(5.5\pm 0.7)\times 10^{-8}\,\mathrm{rad\,d}^{-2}$ for (138852) 2000 WN10. The analysis of Ra-Shalom also reveals a precession of the spin axis with a precession constant $\sim 3000''\,\mathrm{yr}^{-1}$. This is the first such detection from Earth-bound photometric data. For the other two asteroids, we improved the accuracy of the previously reported YORP detection: (i) $(4.94 \pm 0.09)\times 10^{-8}\,\mathrm{rad\,d}^{-2}$ for (1862) Apollo, and (ii) $(1.86\pm 0.09)\times 10^{-8}\,\mathrm{rad\,d}^{-2}$ for (161989) Cacus. Despite the recent report of a detected YORP effect for (85989) 1999 JD6, we show that the model without YORP cannot be rejected statistically. Therefore, the detection of the YORP effect for this asteroid requires future observations. The spin-axis precession constant of Ra-Shalom determined from observations matches the theoretically expected value. The total number of asteroids with a YORP detection has increased to 12. In all cases, the rotation frequency increases in time.
