{-15, 5}

Explanation

The absolute value of 5 plus a number equals 10 should be written as |5 + x| = 10. Absolute value means the distance of a number from zero, so whenever you solve for the number inside absolute value bars, you must consider both the positive and negative values. Take away the bars and set the expression equal to both 10 and -10. 5 + x = 10 gives you x = 5, and 5 + x = -10 gives you x = -15. The solution set is x = {-15, 5}.

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