This article examines the capacity performance of millimeter-wave (mmWave) communication systems utilizing multiple reconfigurable intelligent surfaces (RISs). Specifically, transceiver hardware impairments (THI) at both source and destination are taken into account. To dramatically reduce the effects of THI, transmit antenna selection (TAS) is exploited at the source. The mathematical formulas of achievable rate (AR) and energy efficiency (EE) of the considered multi-RIS-mmWave systems with TAS are derived over Nakagami-m channels under the THI conditions. Numerical results clarify the big effects of THI on the AR and EE of the multi-RIS-mmWave systems. It is because the AR and EE with THI are greatly lower than those without THI (without THI is perfect transceiver hardware (PTH)). In this circumstance, utilizing TAS as well as RISs can achieve many benefits. In addition to the combined advantages of TAS and RISs, their individual advantages are also verified. In particular, the AR and EE achieved with TAS are significantly greater than those obtained without TAS. Then, other solutions such as increasing the number of RISs/reflecting elements (REs), rising the number of transmission antennas, and using suitable frequencies and bandwidths are provided to improve the AR and EE of the considered multi-RIS-mmWave systems with TAS and THI. Finally, the AR and EE expressions are verified by Monte-Carlo simulations.