Component for current and voltage amplification
Try something like this behavioral model:



simulate this circuit &ndash; Schematic created using CircuitLab
I'll leave the details of design to you, since you know your application space better. At such high compliance voltages and over such potentially high sink/source currents you will certainly have to do some thermal analysis and make adjustments. You'll also need to select appropriate BJTs that can stand off the required voltages (2N5550 and 2N5401 are examples having \$V_\text{CEO}=150\:\text{V}\$ but not necessarily the dissipation requirements.)
I use the above design with a smaller compliance range (\$\pm 60\:\text{V}\$) and for a much smaller range of currents. So I know it works fine.
And no, I do not know of an OTS option in IC form that handles even a \$\pm 80\:\text{V}\$ compliance range for \$-5\:\text{mA} \le I_O \le 5\:\text{mA}\$. If you find one, please let me know.