Based on Cambridge dictionary the meaning of "a while" is a long time. For example:
You were there quite a while (= a long time), weren't you?
"When did that happen?" "Oh, it was a while ago (= a long time ago).
I haven't seen him for a while (= for a long time).
All of these examples are taken from the mentioned dictionary.
Now my question refers to a case where I want to say to my friend that I called him in 1 up to 5-7 hours ago (let's say that I'm not sure exactly) and I want to say something like "I called you "a while ago" but for short time like I mentioned. Does "some time ago" works here?