Is it safe to run an arduino pro mini 3.3v by 5v? I mean directly connect 5v to vcc not raw pin.
Yes you can.
The only difference between the 3.3 V and 5 V Pro Mini is the crystal and the voltage regulator.
Yes, an 8 MHz resonator-clocked Promini will happily work at 5V vs 3.3V.
If you want, add a diode from VCC to the RAW pin to protect the regulator, altho it's datasheet does not indicate such is warranted. Anecdotally, I used about 10 of these in my fencing club powered from 5V to the VCC line for quite a few years with no such protection and they ran fine for ~ 10 years, until we closed the club.