Explain how the graph of $x>5$ is different from the graph of $x\ge 5$.

Here, use the concept of basic linear inequalities in which we have to know the term inclusion and exclusion of the number which means if a number contains in the equation is $\ge$which the number is also included but if the sign is $>$ which means the number is excluded and in both case equality holds the same.

The graph of the above inequality in real line is:

From the graph it is seen that the line of $x>5$, $5$ is not included in the because an open circle is shown at $5$. So, x includes all numbers greater than $5$.

The graph of the above inequality in real line is:

From the graph it is seen that the line of$x\ge 5$,$5$ is included in this because an closed circle is shown at \[5\]. So, x includes all numbers greater than or equal to $5$.

From the above steps it is clearly seen that the difference in both the inequalities is the inclusion of $5$.