english numbers 1, 2, 3, 4,5

 The answers are only limited by your ability to recognize potential patterns. The most obvious pattern of course is that each number is equal to 1 + the last number, but as you said, the answer is not 6. Here is what I think the second most obvious answer might be:

• The answer is 10. If you are counting in base 6, 6 in base 6 is 10

There are also a wide number of sillier answers you could generate:

• The answer is 1. If the pattern is just 1,2,3,4,5 repeated over and over, it would start over back at 1.
• The answer is 7. The numbers have to contain the letters E or O, so it cannot be 6.
• The answer is 14. The numbers have to alternate between having the letters E and O. Since FIVE has an E, the next number must be FOURTEEN
• The answer is 11, because the number of letters in the numbers has the pattern 3, 3, 5, 4, 4. The next number in that pattern would be 4+2, which is 6, and ELEVEN is the next number that has six letters. The word length pattern would continue: 5, 5, 7, 6, 6, 8 making the next numbers in the sequence 50, 60, 70, 80, 90, and then I don’t believe there is a number after 90 with 8 letters (one-googol has 9.) I like this pattern the most!

At this point my imagination is starting to wear thin, so I’ll leave it to you to find any other patterns!