A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:

32,000 fans x \( \frac{5}{6} \) = \( \frac{160000}{6} \) = 26,667 fans.

The amount of flour you need is (3\(\frac{1}{8}\) - 1\(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{25}{8} \) - \( \frac{12}{8} \)) cups
\( \frac{13}{8} \) cups
1\(\frac{5}{8}\) cups

To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{36}{56} \) = \( \frac{\frac{36}{4}}{\frac{56}{4}} \) = \( \frac{9}{14} \)

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (3 + 5) ÷ 2 x 2 - 5²
P: 2 + (8) ÷ 2 x 2 - 5²
E: 2 + 8 ÷ 2 x 2 - 25
MD: 2 + \( \frac{8}{2} \) x 2 - 25
MD: 2 + \( \frac{16}{2} \) - 25
AS: \( \frac{4}{2} \) + \( \frac{16}{2} \) - 25
AS: \( \frac{20}{2} \) - 25
AS: \( \frac{20 - 50}{2} \)
\( \frac{-30}{2} \)
-15

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{7c^5}{6c^4} \)
\( \frac{7}{6} \) c^{(5 - 4)}
1\(\frac{1}{6}\)c