question about the voltage spec of SN74HC595 .

A typical specification for a 5 V supply is ± 10 %, so it's likely that your V_CC is not guaranteed to have more than 4.5 V. Therefore, this is the voltage for which the datasheet specifies the limits.

If your 5 V supply is actually better than that, try to deduce the limit from figure 12 of SCLA007: HCMOS Design Considerations. However, it might be a better idea to use the 4.5 V value, just to be sure.

To be able to use 3.3 V input signals with a V_CC of 5 V, you need to use a device with TTL-compatible inputs. There is no TTL '595 in the HC family, so you need to go to AHC: SN74AHCT595.

thanks for your quick answer.

I reviewed SN74AHCT595, but the output current is too small (8mA).
Is there any other device with more current?

8 mA is more than the HC's 6 mA.

How much current do you need? What for?

Thanks Clemens Ladisch for your contributions . You are right that TTL compatible devices are needed . The Vih is 0.7*Vcc in general to calculate the Vih levels which is about 3.5V for 5V Vcc . It will be stretching the performance of the device being out of recommended conditions .