We assume the probability on each side is equally probable with probability 1/5. sum=4 has outcomes:{1,4; 2,3; 3,2; 4,1} 4 possible outcomes sum=8 has outcomes:{3,5; 4,4; 5,3} 3 possible outcomes. Total possible outcomes = 5*5=25 there probability of rolling a sum of 4 or 8, by the law of addition, equals 4/25+3/25=7/25
Note: a regular (i.e. fully symmetric) five-sided solid does not exist, so there has to be asymmetry among the probabilities of the five possible outcomes. In addition, it does not have a "top" face, so that makes rolling a five-sided solid a little more difficult to visualize.
