EbS-P got it right. But in addition to that, I'd also down-size the breaker to 15A.
Connecting AWG-12 to a 20A breaker will always be legal, but long runs will have voltage drop issues, which will affect the efficiency and lifetime of the load. For this reason, it is very common to oversize wiring for a given breaker for circuits with long runs.
Specifics will vary (eg. motors vs. lighting), but for general mixed load circuits, the rule of thumb is 2% voltage drop target. In your case, if it is really only 5 amps on this circuit, you would hit that around 140 feet on AWG-12. Allowing 20A on 120 feet of AWG-12 would generate a voltage drop of more than 2x3.5%, no bueno.
AWG-12 on a 15A breaker would be my recommendation.
Note that in saying all of this, I am an electrical engineer, who has never worked a day as a residential electrician. My experience is all industrial high power electronics, and observing what past electricians have done in each of the dozen houses I've lived in or worked on. So, if a true licensed electrician came along and disagreed with me, I'd defer to them, but I don't think they will disagree with my assessment here.
edit: After posting, I noticed that Dan had said 10A, not 5A... not sure why I had the wrong number in my head while responding. At 10A, you will see 1.8% drop on hot and return each, 3.6% apparent voltage. Not fantastic, the standard published de-rating tables for 2% drop list AWG-10 for 115 feet at 10 amps, and only 70 feet on AWG-12. Depending on the type of load, you will want to make a decision between these two, as per what level of voltage drop is acceptable. For example, if the load is rated to run on 110V-120V, and your panel holds steady at 120V, then you're covered at AWG-12.