I just buy a brand new Pi5 and wonder if I can use this supply before get the New 27W 5.1v=5A supply for PI5 from Amazon
Is there any risk to damage anything on the board from this charger?
The only way you can damage the Pi with a power supply is if it is an inappropriate voltage (or is somehow broken/defective, etc.). That looks to be a smart adapter which will work with the Pi's USB-C port to supply the correct 5V and 3A of current, which should be fine as long as you are not using any USB peripherals beyond a mouse and keyboard.
If it cannot provide enough current, the Pi either won't start properly1 or will report low voltage if you ask it via sudo vcgencmd get_throttled (since insufficient current will cause the system voltage to drop). This will spit out a hex value (eg. throttled=0x1234). These are explained here;
take it and:
echo $((0x1234 & 0x10001))
The first value is whatever throttled= was. The second value should be as shown. If you get 1, 65536, or 65537 back, you have a voltage problem and should shut the Pi down and stop using the supply. If you get 0, the voltage is fine (if the original value was 0x0, everything is fine).
The "undervoltage has occurred" value, once set, remains so until the system is shut down, so you should check this periodically.