The failure rate of condoms is around 3%. Consider a standard box of 12. Let x be the number of failures. Create probability distribution.

The table I created is

0 0.693842361 0.694
1 0.257508505 0.258
2 0.043802993 0.044
3 0.004515772 0.005
4 0.000314242 0.000
5 1.55501E-05 0.000
6 5.61087E-07 0.000
7 1.48742E-08 0.000
8 2.87516E-10 0.000
9 3.95211E-12 0.000
10 3.66691E-14 0.000
11 2.06199E-16 0.000
12 5.31441E-19 0.000

Is this table correct? What is the probability that between 5-10 will fail?
By looking at the table, if is correct, it would indicate that is zero.

The probability that between 5 and 10 will fail is given by:

\sum_{k=5}^{10}C(12,k)(.03)^{k}(.97)^{12-k}=.0000678

or about .00678%

The table is correct, except that in the 2nd column you have rounded the numbers so that anything less than 10^(-4) shows as zero - why did you do that? Sum up the entries in the first column for the range from 5 to 10 and you'll get the answer.