To find f5(2), we need to calculate the functions step by step, starting from f1 and moving up to f5.

First, we calculate f1(2):
f1(x) = 2x - 1
f1(2) = 2*2 - 1 = 4 - 1 = 3

Now, we use the result of f1(2) to find f2(2):
fn(x) = f1(fn-1(x))^2 + sin(x)
f2(x) = f1(f1(x))^2 + sin(x)
f2(2) = f1(f1(2))^2 + sin(2)
f2(2) = f1(3)^2 + sin(2)
f2(2) = (2*3 - 1)^2 + sin(2)
f2(2) = (6 - 1)^2 + sin(2)
f2(2) = 5^2 + sin(2)
f2(2) = 25 + sin(2)

Next, we calculate f3(2):
f3(x) = f1(f2(x))^2 + sin(x)
f3(2) = f1(f2(2))^2 + sin(2)
f3(2) = f1(25 + sin(2))^2 + sin(2)
f3(2) = (2*(25 + sin(2)) - 1)^2 + sin(2)
f3(2) = (50 + 2*sin(2) - 1)^2 + sin(2)
f3(2) = (49 + 2*sin(2))^2 + sin(2)

Then, we find f4(2):
f4(x) = f1(f3(x))^2 + sin(x)
f4(2) = f1(f3(2))^2 + sin(2)
f4(2) = f1((49 + 2*sin(2))^2 + sin(2))^2 + sin(2)
f4(2) = (2*((49 + 2*sin(2))^2 + sin(2)) - 1)^2 + sin(2)
f4(2) = (98 + 4*sin(2) + 2*sin(2) - 1)^2 + sin(2)
f4(2) = (97 + 6*sin(2))^2 + sin(2)

Finally, we calculate f5(2):
f5(x) = f1(f4(x))^2 + sin(x)
f5(2) = f1(f4(2))^2 + sin(2)
f5(2) = f1((97 + 6*sin(2))^2 + sin(2))^2 + sin(2)
f5(2) = (2*((97 + 6*sin(2))^2 + sin(2)) - 1)^2 + sin(2)
f5(2) = (194 + 12*sin(2) + 2*sin(2) - 1)^2 + sin(2)
f5(2) = (193 + 14*sin(2))^2 + sin(2)

To get the numerical value of f5(2), we need to calculate sin(2) and then substitute it into the expression for f5(2). Let's calculate sin(2) using a calculator:

sin(2) ≈ 0.9092974268

Now we substitute sin(2) into the expression for f5(2):
f5(2) = (193 + 14*0.9092974268)^2 + 0.9092974268
f5(2) = (193 + 12.7301635752)^2 + 0.9092974268
f5(2) = (205.7301635752)^2 + 0.9092974268
f5(2) ≈ 42347.080 + 0.9092974268
f5(2) ≈ 42347.9892974268

Therefore, f5(2) is approximately 42347.9892974268.
f5(2)를 찾으려면 f1에서 시작하여 f5까지 단계별로 함수를 계산해야 합니다.

먼저 f1(2)를 계산합니다:
f1(x) = 2x - 1
f1(2) = 2*2 - 1 = 4 - 1 = 3

이제 f1(2)의 결과를 사용하여 f2(2)를 찾습니다:
fn(x) = f1(fn-1(x))^2 + sin(x)
f2(x) = f1(f1(x))^2 + sin(x)
f2(2) = f1(f1(2))^2 + sin(2)
f2(2) = f1(3)^2 + sin(2)
f2(2) = (2*3 - 1)^2 + sin(2)
f2(2) = (6 - 1)^2 + sin(2)
f2(2) = 5^2 + sin(2)
f2(2) = 25 + sin(2)

다음으로 f3(2)를 계산합니다:
f3(x) = f1(f2(x))^2 + sin(x)
f3(2) = f1(f2(2))^2 + sin(2)
f3(2) = f1(25 + sin(2))^2 + sin(2)
f3(2) = (2*(25 + sin(2)) - 1)^2 + sin(2)
f3(2) = (50 + 2*sin(2) - 1)^2 + sin(2)
f3(2) = (49 + 2*sin(2))^2 + sin(2)

그런 다음 f4(2)를 찾습니다:
f4(x) = f1(f3(x))^2 + sin(x)
f4(2) = f1(f3(2))^2 + sin(2)
f4(2) = f1((49 + 2*sin(2))^2 + sin(2))^2 + sin(2)
f4(2) = (2*((49 + 2*sin(2))^2 + sin(2)) - 1)^2 + sin(2)
f4(2) = (98 + 4*sin(2) + 2*sin(2) - 1)^2 + sin(2)
f4(2) = (97 + 6*sin(2))^2 + sin(2)

마지막으로 f5(2)를 계산합니다:
f5(x) = f1(f4(x))^2 + sin(x)
f5(2) = f1(f4(2))^2 + sin(2)
f5(2) = f1((97 + 6*sin(2))^2 + sin(2))^2 + sin(2)
f5(2) = (2*((97 + 6*sin(2))^2 + sin(2)) - 1)^2 + sin(2)
f5(2) = (194 + 12*sin(2) + 2*sin(2) - 1)^2 + sin(2)
f5(2) = (193 + 14*sin(2))^2 + sin(2)

f5(2)의 값을 구하려면 sin(2)를 계산한 다음 f5(2)의 표현식에 대입해야 합니다. 계산기를 사용하여 sin(2)를 계산해 보겠습니다:

sin(2) ≈ 0.9092974268

이제 sin(2)를 f5(2)의 표현식에 대입합니다:
f5(2) = (193 + 14*0.9092974268)^2 + 0.9092974268
f5(2) = (193 + 12.7301635752)^2 + 0.9092974268
f5(2) = (205.7301635752)^2 + 0.9092974268
f5(2) ≈ 42347.080 + 0.9092974268
f5(2) ≈ 42347.9892974268

따라서 f5(2)는 약 42347.9892974268입니다.