from some mistake I connect 5V to GND and arduino board just power off ! can this short cause some problems to the board?
This is a normal thing. The light goes off because the Arduino is "suffering" from the high current and resets. You have done this one time, try not to do it again. Short exposures are Ok but its better to avoid them. However, long exposure between the 5v and GND may lead to a broken board so try not to repeat it.
Thank you for your advice! I will try to avoid these mistakes in the future because I don't want to damage my board
- Shorting a power supply should absolutely never be considered "Ok". Don't do it.
- You should absolutely never change connections while powered.
Experience has shown me everyone ignores #2 until they finally blow up something they can't afford to replace.
And as a corollary to that, there was a thread recently suggesting always to load a sketch like bare minimum each time you're done, so that next time you power up you don't have to scratch your head wondering what pins are doing what. My bare minimum also puts pin 13 low- that LED is often on after a power up.