Let the random variable \(X\) represent the number of days Jake completes the puzzle in 5 days. \(X\) follows a binomial distribution with parameters \(n = 5\) and \(p = 0.75\).

We need to find \(P(X \geq 3)\), which is \(P(X = 3) + P(X = 4) + P(X = 5)\).

Using the binomial probability formula \(P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}\):

\(P(X = 3) = \binom{5}{3} (0.75)^3 (0.25)^2 = 10 \times 0.421875 \times 0.0625 = 0.26367\)

\(P(X = 4) = \binom{5}{4} (0.75)^4 (0.25)^1 = 5 \times 0.31640625 \times 0.25 = 0.39551\)

\(P(X = 5) = \binom{5}{5} (0.75)^5 (0.25)^0 = 1 \times 0.2373046875 \times 1 = 0.23730\)

Adding these probabilities gives:

\(P(X \geq 3) = 0.26367 + 0.39551 + 0.23730 = 0.896\)