To determine the cost for 5 tickets based on the given piecewise function \( f(x) \), we need to first identify the appropriate cost per ticket based on the range of \( x \).
Since Grace and her family are buying 5 tickets, we need to see where this falls under the defined ranges:
- For \( 1 \leq x \leq 5 \), the cost per ticket is \( 35 \).
- For \( 6 \leq x \leq 10 \), the cost per ticket is \( 30 \).
- For \( x \geq 11 \), the cost per ticket is \( 25 \).
Since \( 5 \) (the number of tickets) falls within the first range (\( 1 \leq x \leq 5 \)), the cost for one ticket is \( 35 \).
Now, calculate the total cost for 5 tickets:
\[ \text{Total Cost} = \text{Number of Tickets} \times \text{Cost per Ticket} \] \[ \text{Total Cost} = 5 \times 35 = 175 \]
Therefore, the total cost for 5 tickets will be $175.