According to the New Zealand Ministry of Business, Innovation, and Employment (pdf), the average home in New Zealand uses 7,046 kWh per year, and pays a rate of $0.2879/kWh (NZD).
I used this as a starting point to set up a simulated solar array using PVWatts, a very useful tool developed by the U.S. National Renewable Energy Lab.
I set up a system for Wellington, New Zealand, with the following parameters. For your purposes you'd want to determine the correct values for your proposed system and utility, and adjust the highlighted parameters accordingly. I set the azimuth to 0 degrees, meaning the simulated system is facing due north, which I assume would be optimal for a solar array in the southern hemisphere.
With a bit of trial and error I determined that the optimal tilt for such a system is 32 degrees. The outputs for this system, and an identical system at 5 degree tilt, are:
32 degree tilt: 1,318 kWh $380
5 degree tilt: 1,211 kWh $348
107 kWh $ 32
Thus the optimal tilt improves output by about 8%, equating to about $0.32 NZD per watt.
If we ignore the time value of money and assume a 20 year lifespan, you'd have
$0.32 x 20 = $6.40 to spend on labor and materials (per watt) for setting up racking at 32 degrees, or additional panels. With quotes for panels and racking installation, you could quickly determine which approach made the most sense -- though I suspect the answer will be more panels.