The sequence $S_1,S_2,S_3,\dots ,S_{10}$ has the property that every term beginning with the third is the sum of the previous two. That is, $S_n=S_{n-2}+S_{n-1}\text{ for }n\ge 3.$ Suppose that $S_{10}=233$ and $S_8=89$. What is $S_5$?