How can I draw a circuit from its transfer function?
Here's a fairly straightforward hint or two....

Split the function into simpler parts like: -

\$G(s) = \dfrac{1}{s+1}\times \dfrac{1}{s+5}\times 10\$

Each simpler part is a functional block and when functional blocks are placed in series they multiply to give \$G(s)\$.

So, the easy one is a gain of ten block but how do you implement \$\dfrac{1}{s+1}\$. 

Take a look at what a simple low pass filter does formed by a resistor and capacitor: -



Now I'm mentioning the RC LPF because I recognized it has a transfer function similar to \$\dfrac{1}{s+1}\$. You can go and derive it if you want but there is enough info on the web to tell you that it is: -

\$\dfrac{V_O}{V_I} = \dfrac{\frac{1}{CR}}{s+\frac{1}{CR}}\$ if CR = 1 then you have one of the parts. 

Hints over.

BTW, as an addition I think it can be done with two op-amps but if you want to use 5 there's nothing stopping you except the shame of it!