The best conclusion I can make is that the junction is badly designed, since so many of us have different answers!!

If you go into street view and zoom in more it becomes clear.  There is a clearly denoted traffic light controlled pedestrian crossing past the side street.  One can turn right into Rimu St prior to the stop lines associated with the lights.

The aerial photos are older and don't show the lights ... just a pedestrian island

I travel through these lights minimum twice daily and can confirm you are legally allowed to turn right in this particular instance.

A pedestrian crossing here is often a very welcome event as it can be hard crossing in to Rimu street during busy periods.  Typical Auckland drivers traveling from Great North Road like blocking the entrance.

You were beeped at because a red light is precious to people piling up on the center median strip.

If you're going up this road just to get back to Great North Road, it's often faster to just take the main intersection.  It's a constant argument amongst peers here, but I insist their "shortcut" is actually a "longcut" haha.

My vote is it is OK to turn right,

The Red lights are not controlling the intersection,only the pedestrian crossing, ( i.e You can enter the intersection without having to pass a red/orange/green set of ights) 

DravidDavid:

 

I travel through these lights minimum twice daily and can confirm you are legally allowed to turn right in this particular instance.

 

A pedestrian crossing here is often a very welcome event as it can be hard crossing in to Rimu street during busy periods.  Typical Auckland drivers traveling from Great North Road like blocking the entrance.

 

You were beeped at because a red light is precious to people piling up on the center median strip.

 

If you're going up this road just to get back to Great North Road, it's often faster to just take the main intersection.  It's a constant argument amongst peers here, but I insist their "shortcut" is actually a "longcut" haha.

 

You got it bro. My supervisor was on my car suggested to take the "shortcut"... and he cannot explain this properly. LMAO

Can somebody explain why there is 5 sets of lights in basically the same place?

Is that a bit too many or am I missing something here?

I dont know why there are lights on the right hand side of the road, if it has nothing to do with turning into rimu st?

Yes, as above, it seems you can turn right. The drawing in the OP missed the detail. I believe that the way the road is painted is trying to indicate this, but possibly could be clearer with signage. Perhaps not the best place for a crossing!

Finch:

 

Can somebody explain why there is 5 sets of lights in basically the same place?

 

Is that a bit too many or am I missing something here?

 

I dont know why there are lights on the right hand side of the road, if it has nothing to do with turning into rimu st?

 

I think there are actually six lights, with one facing away from you in the above pictures. Pretty much standard layout for a controlled pedestrian crossing or any intersection on a long fairly busy road. 

Why are there no zebra stripes on the road to mark the crossing?

Geektastic:

 

Why are there no zebra stripes on the road to mark the crossing?

 

Because it's controlled by traffic lights, and not an uncontrolled pedestrian crossing?

JayADee: Man that is confusing! Why are there so many lights?
Is that a one way street?

Perhaps it's a standard traffic light configuration for the class of road? Look at other sets of traffic lights along the same road. Pretty sure they have a format/configuration that has to be followed (like most road signage). And no, it's a two way street.

Not sure why there's confusion to be honest. It IS in Auckland after-all!

Stu:

 

JayADee: Man that is confusing! Why are there so many lights?
Is that a one way street?

 

Perhaps it's a standard traffic light configuration for the class of road? Look at other sets of traffic lights along the same road. Pretty sure they have a format/configuration that has to be followed (like most road signage). And no, it's a two way street.

 

Lake Road in Devonport has an almost identical configuration for the pedestrian crossing, its just 2 lanes instead of 4 so hence why it only has/needs one high light.

https://www.google.co.nz/maps/@-36.8232168,174.7977074,3a,75y,172.58h,79.04t/data=!3m6!1e1!3m4!1sbeZDXKrRT-2Y6P04oBsmMA!2e0!7i13312!8i6656