The sum of the interior angles of any polygon is

 (N-2)180° 

where N is the number of sides (and interior angles).  

In the case of a pentagon, N=5, so the sum of the 
5 interior angles is

(5-2)180° = (3)180° = 540°.

Let the angles be A, B, C, D, and E.  Then

A + B + C + D + E = 540

Let's see if all 5 can be acute:

A < 90°
B < 90°
C < 90°
D < 90°
E < 90°

Adding all those inequalities:

        A < 90°
        B < 90°
        C < 90°
        D < 90°
        E < 90°
---------------
A+B+C+D+E < 450°

No, since that sum must equal 540°,
not less that 450°. But we could make
4 of them, A, B, C, and D acute, 

        A < 90°
        B < 90°
        C < 90°
        D < 90°
---------------
  A+B+C+D < 360°

and so E would then have to be more than 180°,
which is called a "reflex angle".
for instance

 
Edwin