$ cat ip.txt aabbccddd4444 wccwwtttjjttuu wvccwwtttjjttuu zzxxxwwwmmmnnnn ccwwtttjjttuu
with grep, using extended regex and -x option match only whole line
$ grep -xE '([^w]*w){3}[^w]*' ip.txt | grep -xE '([^t]*t){5}[^t]*' | grep -v 'v' wccwwtttjjttuu
with awk, not sure which versions support {3} regex construct. I tested on GNU awk 4.1.3
$ awk '/^([^w]*w){3}[^w]*$/ && /^([^t]*t){5}[^t]*$/ && !/v/' ip.txt wccwwtttjjttuu
with perl
$ perl -ne '(@w)=/w/g; (@t)=/t/g; (@v)=/v/g; print if $#w==2 && $#t==4 && $#v==-1' ip.txt wccwwtttjjttuu
@w, @t, @v arrays contains all w, t, v characters respectively $#w gives index of last element in @w, so it's value is number of elements minus one