We got some different answers here so I'll solve it myself and hopefully we'll get a two of the same answer.
5[6 ÷ 22 · 3 - 1] ---Write this as a fraction
5[6/22 · 3 - 1] ---Simplify the fraction
5[3/11 · 3 - 1] ---Multiply 3/11 times 3
5[9/11 - 1] ---Rewrite as two fractions
5[9/11- 11/11] ---Subtract
5[-2/11] ---Multiply out
-10/11
CPhill and I both got this answers, so it should be right.