$\mathbb{P} P=5 D^{1} \cdot \frac{(1+i)^{2} i}{(1+1)^{N}-1}$
\(\boxed{P \approx 0.6451612903225806}\)
Step 1 :Given values: \(D = 1\), \(i = 1\), and \(N = 5\)
Step 2 :Plug these values into the formula: \(P = 5 \cdot 1^{1} \cdot \frac{(1+1)^{2} \cdot 1}{(1+1)^{5}-1}\)
Step 3 :Simplify the expression: \(P = 5 \cdot \frac{2^{2}}{2^{5}-1}\)
Step 4 :Calculate the value of P: \(P = 5 \cdot \frac{4}{31}\)
Step 5 :\(\boxed{P \approx 0.6451612903225806}\)