TLDR: the probability is 1/15,125, or 6.6x10^-5%
Each question has five possible solutions, meaning that the probability of selecting the correct answer at random is 20%, one out of the five answers.
Each step forward reduces the probability by 20% of the previous value, so guessing both questions 1 and 2 correctly would be equivalent to 20% of 20%, or 4% so far. This probability can also be expressed as (1/5^n), where 5 represents the available number of choices per problem, and ‘n’ represents the number of problems in the sequence.
So, for five problems, each with five possible answers, the probability of guessing all five correctly becomes (1/5^5), or 1/15,125, or 6.6x10^-5%.