I am trying to design a hydraulic or pneumatic system for a wind turbine. The aim is to drive a pump with the turbine shaft which will be situated on top of a mast to power a motor on the ground, which in turn drives an alternator.
The turbine shaft max rpm will be 150 giving 10 kw`s of power at that speed.
The alternator needs to spin at 5000 rpm for max efficiency although it starts charging at 1000 rpm.

What is the best way to tackle this and which system (Hyd or Air)would be the most suitable.

Do a Google search for "electric generator+wind+hydraulic motor" and look at te info there. Some hits discuss Hydraulic drives.

I believe a system like you advocate would be only about 60% efficient with the least flow restrictions you could obtain. With undersized lines and typical hydraulic oil the Cold Weather eficiency would be even less.

Hydro-Static circuitts are better used in Low RPM High Torque Appliations and where bi-directional drive is required.

Perhaps is the problem not the hydro or pneumatic solution but putting the power into the electrical network, do you have an idea on this? Electrical network providers don't like it much, they receive peaks on times they don't need it etc. Do you have a solution and permission to connect the whole system to the electrical network, if you are connecting it of course? It can be expensive to connect it on an electrical network.