Hose number 5 -- arrow point at -- is the one that I can not locate. About 14 inches long, no branching, goes to auxiliary water pump?.

I have removed the fairly simple hose that runs to the auxiliary pump (I think that is it).. The Jaguar parts guy could not find a parts number with this diagram and the hose in hand. I have not seen it on other images online. I do hope someone can please help.
BTW. The lower connecting clamp is reached by removing the front passenger side wheel (US), the wheel well guard, and a bit of rubber shield so you can come in from the wheel area.

 

Car is a 2005 S Type R

 

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The item labelled as number five is the auxiliary pump. If you need the hose that attaches to the top of the pump, the JLR part number is XR851819. See the illustration above.

 

Thanks so much. Like many here, we have to deal with hoses on a regular basis. Looks like mine is the XR851819 and it has been ordered.

 

Just a suggestion from a former 2005 STR owner?

Look at the diagram you posted. It is very complicated and there are 22 or 23 hoses.
If you have not done so replace ALL the rubber coolant hoses. This ones pretty deep so you will be part way there already.
I had 3 separate hose leaks/replacements before I finally did them all. It was really the only failure of importance I had on that car.

Also consider the water pump. Easy to change and not expensive. Mine lasted to about 120K miles.

Finally you don't mention the big one? The hose under the SC.
Has it been replaced?
.
.
.

 

Received the part today. It is wrong. I ordered xr851819 based on my VIN. The hose is shaped wrong and is about 5 inches too long. I just ordered another part from a guy at Walnut Creek Jaguar who used the original part number -- the guy in Sacramento could not do that.

 

For future use here is a link to the official on-line Jaguar parts catalogue on the jaguar Classic Parts UK website:

https://www.jaguarclassicparts.com/uk/s-type-parts

The part you need is listed under the Air Conditioning/Heating/Ventalation section in sub-section 'Pipes and hoses' and sub-sub section ' Water Valve, Pump and Hoses-Petrol'

Here is a direct link to that web page:

https://www.jaguarclassicparts.com/u...d-hoses-petrol

Please note that there is a change of part number for this pipe at vin N52048. This is the start of the 06 model year.

Mellow