When I try and run the avrdude.exe from C:\ARDUINO\arduino-1.0.5\hardware\tools\avr\bin directory the dos window opens and immediately closes.
If I try RUN then CMD and select the path dos window stays but I can't get to run the program in terminal mode. It just gives me the list of options and closes.
avrdude is a command line application. If you double-click on it, it'll run with no parameters, which (as JH says) usually spits out a "you didn't do it right -- here's the usage:" page and exits.
Correct way is to open a command prompt window, navigate your way to the directory (or add it to your path) and run it by name from there.
Not only that, but it's a UNIX-style command-line application. So it expects all of its arguments on the command line; if you run it with no arguments, or not enough arguments, it will just spit out a relatively unhelpful message (hey, it's traditional!) and quit.
And in typical Unix fashion, the official documentation takes a good reading to understand. Don't expect to skim to the first example command line and be able to take off running!