cryptography - RSA and extended euclidian algorithm

I'm learning about RSA, public private key stuff, and I just found a very nice article explaining the basics.

http://arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/

Let's make this more concrete with an example. Take the prime numbers 13 and 7. Their product gives us our maximum value of 91. Let's take our public encryption key to be the number 5. Then using the fact that we know 7 and 13 are the factors of 91 and applying an algorithm called the Extended Euclidean Algorithm, we get that the private key is the number 29.

I can't seem to make sense out of that. How do we get that 29?