After you subtract $5$ from both sides, you will have an inequality involving $-3t$. When you divide both sides by $-3$, what must you do to the inequality sign?

Once you have a condition like $t < \text{(some number)}$ or $t > \text{(some number)}$, compare each answer choice to that condition and eliminate any that do not fit.

In Desmos, use $x$ in place of $t$. Type 5 - 3x > 11 into an expression line. Desmos will shade the region on the $x$-axis that represents all $x$-values satisfying the inequality.

Look along the $x$-axis and see which of the values $-2$, $0$, $3$, and $-5$ lie in the shaded region. Any value that is in the shaded region is a solution to the inequality; any value outside is not.

Write the inequality:

To start isolating $t$, subtract $5$ from both sides:

which simplifies to

Now divide both sides by $-3$, the coefficient of $t$.

Because you are dividing by a negative number, you must flip the inequality sign:

So all values of $t$ that are less than $-2$ satisfy the inequality.

Now compare each option to the condition $t< -2$:

• $-2$ is not less than $-2$ (it is equal), so it does not work.
• $0$ and $3$ are greater than $-2$, so they do not work.
• $-5$ is less than $-2$, so it satisfies the inequality.

Therefore, the value of $t$ that satisfies $5 - 3t > 11$ is $\boxed{-5}$.