SMO 2009 Junior Round 2 Question 5

Let $a,b$ be positive real numbers satisfying $a+b=1$. Show that if $x_1,x_2,\ldots,x_5$ are positive real numbers such that $x_1x_2\cdots x_5=1$, then $$(ax_1+b)(ax_2+b)\cdots(ax_5+b)\ge1.$$