The answer is "is". This is a grammar question not a math one. It is true that 7+5 is 12 and not 13, but that is irrelivant.
No and yes. Yes, this can be viewed as a grammar question, however you need to review your grammar rules.
As a grammar question the answer is "are". It is not correct to say two objects together are singular. Seven AND five denote a group of two objects. Singular uses "is", plural uses "are".
Example: A pen and a pencil ARE on my desk. Both objects are singular, together with "and" are plural.
Example: Seven units and five units are thirteen. All numbers are a way of keeping track of something; distance, apples, atoms, some variable, etc.
If it was stated "seven plus five is/are thriteen", the answer would be "is". Seven plus five (or the sum) is a singular result, twelve.
Or another option would be to state it as "the SUM of seven and five is/are thirteen". Sum is singular, therefore uses "is" and that would be correct.
The whole point of this question is to prove your answer. If you say neither, 7+5=12, than you are correct. If you say "are" based on seven AND five denote a group of two objects, and are therefore plural, than you are correct.
If you say "is", that is incorrect grammar and therefore incorrect.