Marisela is putting on a juggling show! She starts with $1$ ball, tossing it once per second. Lawrence tosses her another ball every five seconds, and she always tosses each ball that she has once per second. Compute the total number of tosses Marisela has made one minute after she starts juggling.
1. **Initial Setup:**
   - Marisela starts with 1 ball and tosses it once per second.
   - Lawrence gives her an additional ball every 5 seconds.
   - We need to compute the total number of tosses Marisela has made after 60 seconds.

2. **Determine the Number of Balls Over Time:**
   - At \( t = 0 \) seconds, Marisela has 1 ball.
   - At \( t = 5 \) seconds, Lawrence gives her 1 more ball, so she has 2 balls.
   - At \( t = 10 \) seconds, Lawrence gives her another ball, so she has 3 balls.
   - This pattern continues every 5 seconds.

3. **Calculate the Number of Balls at Each 5-Second Interval:**
   - At \( t = 0 \) seconds: 1 ball
   - At \( t = 5 \) seconds: 2 balls
   - At \( t = 10 \) seconds: 3 balls
   - At \( t = 15 \) seconds: 4 balls
   - At \( t = 20 \) seconds: 5 balls
   - At \( t = 25 \) seconds: 6 balls
   - At \( t = 30 \) seconds: 7 balls
   - At \( t = 35 \) seconds: 8 balls
   - At \( t = 40 \) seconds: 9 balls
   - At \( t = 45 \) seconds: 10 balls
   - At \( t = 50 \) seconds: 11 balls
   - At \( t = 55 \) seconds: 12 balls

4. **Calculate the Total Number of Tosses:**
   - From \( t = 0 \) to \( t = 4 \) seconds, Marisela has 1 ball, so she makes \( 1 \times 5 = 5 \) tosses.
   - From \( t = 5 \) to \( t = 9 \) seconds, Marisela has 2 balls, so she makes \( 2 \times 5 = 10 \) tosses.
   - From \( t = 10 \) to \( t = 14 \) seconds, Marisela has 3 balls, so she makes \( 3 \times 5 = 15 \) tosses.
   - From \( t = 15 \) to \( t = 19 \) seconds, Marisela has 4 balls, so she makes \( 4 \times 5 = 20 \) tosses.
   - From \( t = 20 \) to \( t = 24 \) seconds, Marisela has 5 balls, so she makes \( 5 \times 5 = 25 \) tosses.
   - From \( t = 25 \) to \( t = 29 \) seconds, Marisela has 6 balls, so she makes \( 6 \times 5 = 30 \) tosses.
   - From \( t = 30 \) to \( t = 34 \) seconds, Marisela has 7 balls, so she makes \( 7 \times 5 = 35 \) tosses.
   - From \( t = 35 \) to \( t = 39 \) seconds, Marisela has 8 balls, so she makes \( 8 \times 5 = 40 \) tosses.
   - From \( t = 40 \) to \( t = 44 \) seconds, Marisela has 9 balls, so she makes \( 9 \times 5 = 45 \) tosses.
   - From \( t = 45 \) to \( t = 49 \) seconds, Marisela has 10 balls, so she makes \( 10 \times 5 = 50 \) tosses.
   - From \( t = 50 \) to \( t = 54 \) seconds, Marisela has 11 balls, so she makes \( 11 \times 5 = 55 \) tosses.
   - From \( t = 55 \) to \( t = 59 \) seconds, Marisela has 12 balls, so she makes \( 12 \times 5 = 60 \) tosses.

5. **Sum the Total Number of Tosses:**
   \[
   5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 = 390
   \]

The final answer is \(\boxed{390}\).