What does code P1405 mean ?

I don't know what year or kind of car you have but ford says that P1405 code is a EGR valve problem.

sure.

that is your egr tube coming off the exhaust manifold. they get filled with carbon.. as in the price for the repair that depends where you are ,and most of them break coming off. sending a picture

Follow the link for help with this fault code P1405 Ford DPF EGR Sensor Circuit High Voltage Detected

I suggest you replace the EGR valve position sensor.

Are you sure you have EGR flow?? Hold the EGR valve open the engine should run poorly, if not you have no flow.

check engine light it tied to all the engine control sensors (and more) Larger auto parts outlets will do a free code scan for you. Once you learn what the code is, you can buy a chiltons or haynes manual and determine what the code means and what you need to do to replace that part.

On alot of cars you must erase the code after repairs,the code is pending in the memory and can still run bad till cleared.try clearing the code

It's a very strange code. It shows up in the generic "all manufacturer" code list as "P0601 Internal Control Module Memory Check Sum Error"
Here's a complete list and you can see the GM specific codes on that site as well.

http://www.engine-light-help.com/generic-check-engine-light-codes.html

if you can get the codes... why don't you have a book that comes with the code reader
get yourself a Haynes manual #64200 at your local parts store or online

P1405-Differential Pressure Feedback Electronic (DPFE) sensor upstream hose off or plugged - or cracked.

I believe it is on the driver's side of engine about half-way down. also, check all other hoses for damage