Shrinking the transistor dimensions in complementary metal-oxide-semiconductor (CMOS) technology has led to many huge problems, like high power density. Various methods at different design levels of abstraction, such as approximate computing and spintronic devices based on magnetic tunnel junction (MTJ), have been studied to solve these problems. In this paper, we propose a novel hybrid MTJ/FinFET-based approximate 5:2 compressor. The proposed design employs the spin-transfer torque (STT) method assisted by the spin-Hall effect (SHE) to store inputs in MTJs. Due to the SHE assistance, the energy efficiency of the MTJ switching is improved considerably over the conventional STT method. Our design significantly improves the energy consumption compared to the previous compressors, thanks to the decrease in MTJ and transistor counts. The proposed circuit and previous designs are simulated using HSPICE with 7-nm FinFET and SHE perpendicular-anisotropy MTJ model. From the simulation results, we can see that the proposed design improves power consumption, write energy, read energy, number of transistors and MTJ count on average by 49%, 50%, 63%, 20% and 50%, respectively, in comparison with the existing counterparts. Furthermore, the accuracy of the approximate designs is evaluated through comprehensive MATLAB simulations. The results indicate that the proposed circuit outperforms the best previous energy-efficient designs in terms of accuracy despite having better hardware characteristic parameters.