The equation provided is:

$x^3 - 5x^2 - x + 21 = 0$

To solve this graphically using a graphing calculator, you would plot the function:

$f(x) = x^3 - 5x^2 - x + 21$

on the graph. The real solutions correspond to the x-values where the graph intersects the x-axis (i.e., where $f(x) = 0$).

If you're using a graphing calculator, input the function and look for the points where the graph crosses the x-axis.

Would you like a detailed explanation on how to use the graphing calculator to find the solutions, or would you like me to calculate the solutions here?

Here are 5 related questions to expand your understanding:

1. How does the degree of a polynomial relate to the number of possible solutions?
2. Why do cubic equations always have at least one real solution?
3. What are other methods to solve a cubic equation besides graphing?
4. How does the graph of a cubic function generally behave compared to linear or quadratic functions?
5. Can a cubic equation have exactly two real solutions? Why or why not?

Tip: When solving graphically, ensure your window settings on the graphing calculator allow you to see all potential x-axis crossings.