First, AFCI type breakers can be "touchy", so what I say following doesn't apply.
I did some more Googling.
Apparently manufacturers follow UL standard 489 as to how circuit breakers should behave. There is something called "bulletin 1489" which I think is from ANSI and is similar but not identical.
Here is an Allen-Bradley page on breakers. See the chart at the bottom.
The standards provide some leeway, it's not possible to cost effectively build a breaker that trips exactly at a certain current.
Looking at the chart, see circle #4. That means the breaker must not trip below 500% of max current for at least 0.1 seconds (6 cycles of AC). That's a long long time. A properly behaving power supply will not draw 15x5=75 A of 120 V for 0.1 seconds. It wont. More typically a breaker won't trip for at least 0.7 seconds at 500% of max current. E.g. A-B breakers won't.
See circle #3. That means the breaker must not trip below 200% of max current for at least 10 seconds. It has some leeway. It can take as much as 120 seconds to trip at 200% of max.
So, as
-aggie- said,
"There is no way the extra 4-5 amps from "normal" starting of a computer is going to trip ANY breakers." You either have a touchy AFCI breaker or an older breaker that isn't following the spec.