Extracting sequences from FASTA beginning with common 5' end
Here is a 'quick' python3 solution, requiring installation of BLASTN and a pip3 install biopython.  The results are output in FASTA format to stdout.  

Save the following python3 code in hit_finder.py

#!/usr/bin/env python3

import sys
from Bio import SeqIO
from Bio.Blast.Applications import NcbiblastnCommandline

cline = NcbiblastnCommandline(query=sys.argv[1],
                              subject=sys.argv[2],
                              outfmt="'6 qseqid length qstart'",
                              max_hsps=1,
                              word_size=4)

result = [j[0] for j in [i.split('\t') for i in
                         cline()[0].rstrip().split('\n')] 
          if int(j[1]) &gt;= int(sys.argv[3]) and int(j[2]) &lt;= int(sys.argv[4])]

for record in SeqIO.parse(sys.argv[1], 'fasta'):
    if record.id in result:
        print(record.format('fasta'))


Make it executable: chmod +x hit_finder.py.

This script takes four arguments (which in future versions could be enhanced using argparse instead of sys.argv):

arg1 = query_fasta_file (file to search in)
arg2 = subject_fasta_file (database file to contain the sequence to match at 5')
arg3 = min_alignment_length (this means the length of the hit, allows mismatching in string with blastn and a word_size of 4)
arg4 = start_of_hit_at_5prime (where should the alignment hit start?)


Let's say you wanted to search for AATCTGTAGTACGACTCACTATAGC in your query seqeuences.  Save this sequence in subject.fa as:

&gt;subject
AATCTGTAGTACGACTCACTATAGC


Your query sequences are stored in queries.fa as:

&gt;1-69050-454.08
GTACGGGGAAGGACGTCAATAGTC

&gt;2-65989-433.95
AATCTGTAGTACGACTCACTATAGC

&gt;3-62181-408.91
GATCTGTAATACGACTCACTATAGG

&gt;4-49959-328.53
GGGGAAGGACGTCAATAGTCACAC


Now, to search for hits of at least 23 bp starting no further than 1 base from the 5' end of your sequence, you would run this search using:

./hit_finder.py queries.fa subject.fa 23 1


To search for hits of at least 30 bp no more than 10 bp from the 5' end of your queries, do:

./hit_finder.py queries.fa subject.fa 30 10


To save your results, output stdout to file, e.g.,:

./hit_finder.py queries.fa subject.fa 30 10 &gt; results.fa