Q: Why did my laptop randomly shuts down and start to produce beep sound 3 times with 5 seconds interval

Have you read for possible solutions over in the "More Like This" thread over here?----------------------->

The three beeps are usually indicative of bad RAM. Do the Hardware Test, extended version.

If still within the one-year base warranty period, may want to take it in for assessment before coverage expires. May also want to evaluate whether or not to purchase the AppleCare warranty extension to extend coverage for an extra 2 years.

http://support.apple.com/kb/HT1547  

1 beep = no RAM installed

2 beeps = incompatible RAM types

3 beeps = no good banks

4 beeps = no good boot images in the boot ROM (and/or bad sys config block)

5 beeps = processor is not usable