Just edited the post, I had copied the test in incorrectly - thanks for catching that. I will look into using FindRoot- what if I don't know the initial points to start scanning from though?

FindRoot[{PutTK[95,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==6.45,PutTK[100,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==8.35,PutTK[90,0.001,   \[Sigma],1,\[Gamma],a,b,0.001,.1]==4.93,PutTK[85,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==3.73,PutTK[80,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==2.80},{{\[Sigma],1},{\[Gamma],1},{\[Lambda],1},{a,1},{b,1}}] 

FindRoot gives me the error:

"Encountered a singular Jacobian at the point {[Sigma],[Gamma],\ [Lambda],a,b} = {1.,1.,1.,1.,1.}. Try perturbing the initial point(s)"