You could try

if all([val in string for val in list]):

Which checks the truth of each check and returns True only if all are True. Otherwise you're looking at a loop (or if your lists get really big a generator).

Loop through each sequential set of 5 characters and compute the hamming distance with your key string.

from itertools import tee, islice

def nwise(iterable, n=2):
    """s -> (s0, s1, ..., sn-1), (s1, s2, ..., sn), (s2, s3, ..., sn+1), ...
    Comes from https://stackoverflow.com/a/21303303/5087436"""
    iters = tee(iterable, n)
    for i, it in enumerate(iters):
        next(islice(it, i, i), None)
    return zip(*iters)

def hamming_distance(s1, s2):
    """Returns the number of differences between s1 and s2 (assuming equal length)"""
    return sum(c1 != c2 for c1, c2 in zip(s1, s2))

dna = "ABBACAGTABTAGAAGTBABGTABGTGABAATGBAAGTGBAATTGABAGGTAAGTBAGABAAABGTTAGAAG"
key = "AGTBA"
wildcards = 3

# for each substring with length the same as your key...
for i, seq in enumerate(nwise(dna, len(key))):
    d = hamming_distance(seq, key)
    if d <= wildcards:
        print(f'DNA at index {i}', ''.join(seq), f'matches {key} with distance {d}.')

And this will output something like:

DNA at index 5 AGTAB matches AGTBA with distance 2.
DNA at index 8 ABTAG matches AGTBA with distance 3.
DNA at index 11 AGAAG matches AGTBA with distance 3.
DNA at index 14 AGTBA matches AGTBA with distance 0.
DNA at index 18 ABGTA matches AGTBA with distance 3.
DNA at index 19 BGTAB matches AGTBA with distance 3.
DNA at index 23 BGTGA matches AGTBA with distance 2.
DNA at index 25 TGABA matches AGTBA with distance 2.
DNA at index 29 AATGB matches AGTBA with distance 3.
DNA at index 30 ATGBA matches AGTBA with distance 2.
DNA at index 31 TGBAA matches AGTBA with distance 3.
DNA at index 35 AGTGB matches AGTBA with distance 2.
DNA at index 36 GTGBA matches AGTBA with distance 3.
DNA at index 37 TGBAA matches AGTBA with distance 3.
DNA at index 40 AATTG matches AGTBA with distance 3.
DNA at index 41 ATTGA matches AGTBA with distance 2.
DNA at index 43 TGABA matches AGTBA with distance 2.
DNA at index 47 AGGTA matches AGTBA with distance 2.
DNA at index 48 GGTAA matches AGTBA with distance 2.
DNA at index 52 AGTBA matches AGTBA with distance 0.
DNA at index 56 AGABA matches AGTBA with distance 1.
DNA at index 58 ABAAA matches AGTBA with distance 3.
DNA at index 60 AAABG matches AGTBA with distance 3.
DNA at index 63 BGTTA matches AGTBA with distance 2.
DNA at index 67 AGAAG matches AGTBA with distance 3.

You could also like, sort by the hamming distance and stuff if you wanted too by using it as a key function. This should all be super efficient since it's using iterators and only loops through your key string once per iteration; so it's an O(m*n) operation where m and n are the lengths of your key string and DNA string.

Here's slightly more betterer code IMO (not sure what info is most important, so this has all the major parts); basically, we just add a namedtuple for each match to get better string representation and all the info we could want about any match:

from itertools import tee, islice
from collections import namedtuple


Match = namedtuple('Match', 'start, stop, distance, substring, key, wildcards')


def nwise(iterable, n=2):
    iters = tee(iterable, n)
    for i, it in enumerate(iters):
        next(islice(it, i, i), None)
    return zip(*iters)

def hamming_distance(s1, s2):
    s = sum(c1 != c2 for c1, c2 in zip(s1, s2))
    d = ''.join('*' if c1 != c2 else c1 for c1, c2 in zip(s1, s2))
    return s, d

def findmatches(string, key, nwildcards):
    n = len(key)
    for i, seq in enumerate(nwise(string, n)):
        dist, diffs = hamming_distance(seq, key)
        if dist <= nwildcards:
            yield Match(i, i+n, dist, ''.join(seq), key, diffs)


dna = "ABBACAGTABTAGAAGTBABGTABGTGABAATGBAAGTGBAATTGABAGGTAAGTBAGABAAABGTTAGAAG"
key = "AGTBA"
nwildcards = 3

for m in findmatches(dna, key, nwildcards):
    print(m)

And this would produce output like:

Match(start=5, stop=10, distance=2, substring='AGTAB', key='AGTBA', wildcards='AGT**')
Match(start=8, stop=13, distance=3, substring='ABTAG', key='AGTBA', wildcards='A*T**')
Match(start=11, stop=16, distance=3, substring='AGAAG', key='AGTBA', wildcards='AG***')
Match(start=14, stop=19, distance=0, substring='AGTBA', key='AGTBA', wildcards='AGTBA')
Match(start=18, stop=23, distance=3, substring='ABGTA', key='AGTBA', wildcards='A***A')
Match(start=19, stop=24, distance=3, substring='BGTAB', key='AGTBA', wildcards='*GT**')
Match(start=23, stop=28, distance=2, substring='BGTGA', key='AGTBA', wildcards='*GT*A')
Match(start=25, stop=30, distance=2, substring='TGABA', key='AGTBA', wildcards='*G*BA')
Match(start=29, stop=34, distance=3, substring='AATGB', key='AGTBA', wildcards='A*T**')
Match(start=30, stop=35, distance=2, substring='ATGBA', key='AGTBA', wildcards='A**BA')
Match(start=31, stop=36, distance=3, substring='TGBAA', key='AGTBA', wildcards='*G**A')
Match(start=35, stop=40, distance=2, substring='AGTGB', key='AGTBA', wildcards='AGT**')
Match(start=36, stop=41, distance=3, substring='GTGBA', key='AGTBA', wildcards='***BA')
Match(start=37, stop=42, distance=3, substring='TGBAA', key='AGTBA', wildcards='*G**A')
Match(start=40, stop=45, distance=3, substring='AATTG', key='AGTBA', wildcards='A*T**')
Match(start=41, stop=46, distance=2, substring='ATTGA', key='AGTBA', wildcards='A*T*A')
Match(start=43, stop=48, distance=2, substring='TGABA', key='AGTBA', wildcards='*G*BA')
Match(start=47, stop=52, distance=2, substring='AGGTA', key='AGTBA', wildcards='AG**A')
Match(start=48, stop=53, distance=2, substring='GGTAA', key='AGTBA', wildcards='*GT*A')
Match(start=52, stop=57, distance=0, substring='AGTBA', key='AGTBA', wildcards='AGTBA')
Match(start=56, stop=61, distance=1, substring='AGABA', key='AGTBA', wildcards='AG*BA')
Match(start=58, stop=63, distance=3, substring='ABAAA', key='AGTBA', wildcards='A***A')
Match(start=60, stop=65, distance=3, substring='AAABG', key='AGTBA', wildcards='A**B*')
Match(start=63, stop=68, distance=2, substring='BGTTA', key='AGTBA', wildcards='*GT*A')
Match(start=67, stop=72, distance=3, substring='AGAAG', key='AGTBA', wildcards='AG***')