Where can I find Boeing 777 safety records?
The Boeing 777 has an excellent reputation when it comes to safety.

Just under 1500 have been built which have accumulated more than five million flights and 20 million flight hours.
Only 6 aircraft have been lost in a accident, which is a really low number considering the number of aircraft and flights. 

Moreover, of those hull losses, at least one (MH17) was due to a criminal act which cannot be attributed to the safety of this specific aircraft type.

Of the other 5 hull losses:


One cause is unknown (MH370). 
One (MS667) was caused by fire while the aircraft was at the gate. No fatalities. 
Three crashes were during landing. 


Of the three crashes during landing:


One (BA038) is caused by ice in the fuel system which clogged a filter. The filter has been redesigned and can no longer cause a problem. The accident did injure 47 people, there were no fatalities. 
One (OZ214) was caused by the pilots committing a number of minor and major errors during the approach to the airport. It can hardly be attributed to the aircraft type. The crash resulted in only 3 fatalities, which is remarkable considering the violence of the crash and amount of damage to the aircraft. 
The last accident (EK521) caused no fatalities among the passengers but the cause of the accident is still under investigation. So far, the  Investigation  is  working  to determine  and analyze  the  human  performance  factors  that  influenced  flight  crew  actions  during  the  landing and attempted  go-around. The investigation has revealed no  Aircraft systems  or  engine  abnormalities  up  to  the  time  of the  Accident. 


Combined you can see that the aircraft has performed an enormous number of flights with very few severe accidents and very few fatalities. 

It is considered as one of the safest aircraft around.