The two bases of any prism must be congruent. That means they are the same size and the same shape. If they are oriented perpendicularly to the sides, one base directly above the other so that their connecting sides are rectangles, that is a right prism. If the bases are oriented at a different angle so that the connecting sides are parallelograms, but not rectangles, that is an oblique prism. This applies to pentagonal prisms as well as any other type pf prism.
A regular polygon has sides all of the same length, and all internal angles equal. The Pentagon, seen from above, is a regular pentagon. All five sides are the same length, and all internal angles are the same (108 degrees). If you were to take a square and remove the top side, and replace it with an upside down V, that would still be a pentagon, but it would not be a regular pentagon. A prism with regular bases is a regular prism. A prism with irregular bases is an irregular prism.
The volume of a prism is simply the area of the base multiplied by the height of the prism. If it's an oblique prism, the height is equal to the sine of the angle between the base and parallelogram sides, multiplied by the length of the parallelogram side. For a right prism, the angle is 90 degrees, the sine of which is 1, so the height is the same as the length of a side.
You still need to find the area of the pentagonal base in order to find the volume of your entire pentagonal prism, and that's more complicated than it may appear at first glance. For any regular polygon, the formula to determine the area is ½ nsr where n = number of sides, s = the length of a side, and r = the length of the apothem. The apothem is the distance from the center of the polygon to the midpoint of one of the sides. Use this formula: r = s / 2 * tan (pi/n). It's important to remember that when you take the tangent of pi/n, that you are using radians, and not degrees. If you had a regular pentagon with sides of one unit length, the area would be approximately 1.7204.