The sum of two numbers is 23. Seven times the first number less five times the second number is equal to 5. What are the two numbers?

Now, i have worked this out and the numbers i get equal 23 but are not the numbers given as the answer in the book. Take a look:

x + y = 23

7x - 5y = 5

7(23 - y) - 5y = 5

161 - 7y - 5y = 5

161 - 2y = 5

2y = 156

y = 78

Put the numbers into the equation: -55 + 78 = 23

So the answer i get appears to be correct because it works. But like i said, the answer in the back of the book is 10 + 13 = 23

So where did i go wrong? And if algebra lead me to my answer (-55 + 78 = 23) which makes the equation true, why can't my answer be the right answer?