Gnomes are trouble #1

One fine spring day Harlow decided to visit his cousin Alber who lived in the next valley. Harlow liked visiting Alber but dreaded traveling over the mountain pass to reach Alber’s village. The pass was in the land of the gnomes and they always made mischief for pnomes traveling through it.

Harlow was almost at the top of the pass. So far so good. No sign of mischief from the gnomes. Just as Harlow reached the top, a heavy wooden cage dropped from an overhanging pine branch and trapped him inside. To make matters worse he had to listen to noisy giggles coming from behind the pine tree. Harlow wasn’t really trapped of course. The gnomes always allowed someone a way out of their mischief.

The cage had two compartments. Harlow was trapped in the first compartment. There was a lock with numbers and a pointer on the door between the first and second compartment. All Harlow had to do was to set the pointer to the correct number and the lock would open. But what was the correct number? The gnomes had left a clue in the form of strange looking number sentences scribbled on a piece of paper tacked to the door.

5 & 1 = 5
6 & 2 = 7
8 & 4 = 11
6 & 5 = __

“Ah”, thought Harlow, “I just need to figure the answer to 6 & 5 and set to pointer to that number. But what is the answer? There must be a pattern in the examples. Let me think. Let me think.”