Print line based on partial match

I have two files with several hundred entries in each. File 1 has several 5 base seqeunces and file 2 has higher number of entries but with longer sequences. The first 5 bases of sequences in file 2 matches that of file 1. I tried some grep and awk methods , but did not work out for a partial match case as above. So for example:

File 1:

       ATGCC
       TTGCA
       GGAAC

........
........

File 2:

ATTTCGGGAAAATT
ATGCCTTAAGACCT
GGAACTAAGGGGA
............
............

Expected outcome:

ATGCCTTAAGACCT
GGAACTAAGGGGA

Any help is much appreciated !
Thanks !