Like all variables the $ will return the value. Seeing as you do not wish to assign it to anything, just remove the $ and all is good with the world. No need for additional items like the colon.
Nice alternative to go with date and as a solution has been presented, here is another:
Code:
#!/bin/bash
while read -a vals
do
[[ ${vals[5]} == 13 ]] && ((cnt++))
[[ ${vals[12]} == 13 ]] && ((cnt++))
[[ ${vals[19]} == 13 ]] && ((cnt++))
done< <(cal -y $1)
echo "Number of black fridays: $cnt"
Again no error checking but here if you omit the date all together it will use the current year
