Well, it's working for me just as you printed it. It could be that your terminal just doesn't support blinking text or something.
BTW, don't forget to set the reset code as well, otherwise all of your console text is going to continue to blink after that (or at least until something you use reconfigures it for you).
Also, if you're trying to set these codes in the shell, then have them available in a script or other sub-process, then you'll have to
export them as well.
Code:
$ export blink='\033[00;05m'
$ export reset='\033[0m'
$ echo -e "${blink}This text is blinking.${reset}"