is it possible to design a complex analog circuit through a predetermined laplace equation?
Write the Laplace TF equation in controller canonical form, then draw the primitive block diagram (in your case there will be five blocks in the forward path, as you have a 5th order equation). Each of the blocks will be an integrator, and each can be realised by an op-amp.

You'll need an additional 2 op-amps to add and subtract signals, plus however many extra ones are required to give the specified DC gain.