I am confused about the slope value. Lets' say we have :
$f(x) = x^3,f(5)=125$
$f'(x)=3x^2,f'(5)=75$
so what they usually say in this situation is that if $x$ increases by $1$ then $y$ will increase by $75$.
So , slope = 75 at $x=5$ I don't quite grasp this value of 75.
The equation of this tangent is $y=75x +b$ and solving for $b$ will result $125=75x+b$ so $b=-250$ and our tangent equation at $x=5$ is $y=75x-250$.
I understand why I need slope only when we are trying to find where is $max$ or $min$ but what useful info gives me if I find slope at let's say $x=3, 5, 1, 6, 100 ...$ and so on ? just for fun ?
Your words: "So what they usually say in this situation is that if $x$ increases by $1$ then $y$ will increase by $75$."
"They" don't say that. What, however, is true is the following:
If $x=5$ then $y=5^3=125$. If $x$ is incremented by a "small" amount $\epsilon$, positive or negative, to $x+\epsilon$ then $y$ undergoes a change of approximately $75\epsilon$ and will be about $125+75\epsilon$.
In precise terms: $$y_{\rm curve}(5+\epsilon)=(5+\epsilon)^3=125+75\epsilon+o(\epsilon)\qquad(\epsilon\to0)\ .$$ On the other hand, if you look at the tangent to the curve at $(5,125)$, a straight line, then you can say that $$y_{\rm tang}(5+t)=125+75 t\qquad(-\infty<t<\infty)\ .$$