To translate and solve the problem 'Nineteen less than $p$ is no less than $47$', follow these sequential mathematical steps:

1. Translate: Deconstruct the sentence into mathematical symbols. The phrase 'nineteen less than $p$' means that $19$ is subtracted from $p$, yielding the expression $p - 19$. The phrase 'is no less than' indicates that the first quantity must be greater than or equal to the second, which is represented by the $\geq$ symbol. Combining these elements provides the inequality $p - 19 \geq 47$.
2. Solve: Isolate $p$ by applying the Addition Property of Inequality. Add $19$ to both sides of the inequality: $p - 19 + 19 \geq 47 + 19$, which simplifies to $p \geq 66$.
3. Graph the Solution: On a number line, indicate that $66$ is included in the solution set by placing a left bracket at $66$, and shade the numerical region to the right to encapsulate all numbers greater than $66$.
4. Interval Notation: The solution set encompasses all real numbers from $66$ up to infinity, formatted in interval notation as $[66, \infty)$.