Where is telephone country code 001513?

00 isn't part of the country code, it is a commonly used international access prefix.

Country code +1 is North America, including USA, Canada, and certain islands.

Area code +1 512 is Austin, Texas, USA.

(The plus sign means "insert your international access prefix here." From a GSM mobile phone, you can enter the number in full international format, starting with the plus sign. The most common prefix is 00, but Japan uses 010, Australia uses 0011, and many other countries use different prefixes.)