total strings with 5 letters= $5^{5}=3125$
strings with no a's= $4^{5}=1024$
strings with one a's= $5*4^{4}=1280$
strings with two a's which are not consecutive= $6*4^{3}=384$
strings with three a's which are not consecutive = $1*4^{2}=16$
after that with 4 and 5 a's you will get atleast two consecutive a's. So
total 5 length strings with two consecutive a's = $3125-1024-1280-384-16=421$
421 strings are there.