To determine how many degrees the temperature fell between 5 P.M. and 10 P.M., follow these steps:
1. Identify the initial temperature: The temperature at 5 P.M. is given as [tex]$20^{\circ} F$[/tex].
2. Identify the final temperature: The temperature at 10 P.M. is given as [tex]$-5^{\circ} F$[/tex].
The temperature fell from [tex]$20^{\circ} F$[/tex] to [tex]$-5^{\circ} F$[/tex] over this period of time.
3. Subtract the final temperature from the initial temperature: To find the fall in temperature, subtract the temperature at 10 P.M. from the temperature at 5 P.M.
[tex]\[
20^{\circ} F - (-5^{\circ} F)
\][/tex]
4. Simplify the expression inside the parenthesis: Subtracting a negative number is equivalent to adding the absolute value of that number.
[tex]\[
20^{\circ} F - (-5^{\circ} F) = 20^{\circ} F + 5^{\circ} F
\][/tex]
5. Perform the addition:
[tex]\[
20^{\circ} F + 5^{\circ} F = 25^{\circ} F
\][/tex]
Therefore, the temperature fell by [tex]\(\boxed{25}\)[/tex] degrees Fahrenheit between 5 P.M. and 10 P.M.
