The ladder must be 5 7/10 high.
First, find the lowest common denominator for 5 and 2. It's 10.
Then, multiply 1/5 times 2 and 1/2 times 5. You will get 2/10 and 5/10.
Next, you have to make them inproper fractions. Multiply 12 times 2/10 and 6 times 5/10. You will get 122/10 and 65/10.
Then, you have to subtract 122/10 minus 65/10. You will get 57/10.
Lastly, you have to change it into a mixed number. Divide 57 and 10. You will get 5 with 7 left over. Your final answer should be 5 7/10.