One of the main rules of tense usage is that the simple past is used for finished actions and especially also with specific expressions of time/in time that point to a specific occasion.
- Five minutes ago
- Ten years ago
- Last week, month, year, yesterday etc.
- Specific dates: October 1st, etc.
For example. There is zero continuity of any kind with the simple past.
Without getting into all the complexity of the present perfect, it is much easier to know, generally speaking, when to use the simple past.
Five minutes ago calls for the simple past.
All expressions with ago and time (five months ago, etc.) call for simple past.
Of course, you can also use: I've just finished my work, but not with five minutes ago.
I sincerely hope this simple rule is clear. When I say rule, I am not talking about standard or non-standard. Even uneducated native English speakers would not mix these up.
The adverb ago refers to a period of time that is completed and goes
from a point in the past up to now. Ago follows expressions of time:
It happened a long time ago.
They arrived in Athens six weeks ago.
Not: They arrived in Athens ago six weeks.
Warning: We normally use ago with the past simple. We don’t use it
with the present perfect: [bolding mine]
I received his letter four days ago.
Not: I have received his letter four days ago.
If we refer to a point in time before a specific time in the past, we
use before or earlier or previously, often with the past perfect:
We had got their invitation four days before.
They met on the same island where they had met ten years previously.
If we refer to how long something lasted, we use for (not ago):
When I was at school, I studied Russian for five years. (my studies
lasted for five years)
Cambridge Dictionary