1. **State the problem:** Solve the inequality $p - 1 + 7 \ge 5 - 1$.\n\n2. **Simplify both sides:** On the left side, combine $-1$ and $7$:\n$$p - 1 + 7 = p + 6.$$\nOn the right side, combine $5$ and $-1$:\n$$5 - 1 = 4.$$\nSo the inequality becomes:\n$$p + 6 \ge 4.$$\n\n3. **Isolate the variable $p$:** Subtract $6$ from both sides to isolate $p$:\n$$p + 6 - 6 \ge 4 - 6,$$\nwhich simplifies to\n$$p \ge -2.$$\n\n4. **Interpret the solution:** The inequality $p \ge -2$ means that $p$ can be any number greater than or equal to $-2$.\n\n**Final answer:** $$p \ge -2.$$