I'm assuming you have done in-depth reading on the Z400 and understand that there are two versions with two Boot Block dates (you can check for that in BIOS). It turns out that a very easy way to know if you have an older version 1 Z400 or the newer motherboard, version 2, is whether you have 4 (older) or 6 (newer) memory sockets. That is the key info you need to know first.
I am running a X5690 on my version 2 Z400. I have no idea whether the processor you mention will work or not. I'm sure it would not work on a version 1, however, so that is the first thing to check out.
I did a quick search for Z400 + X5675 and found ones for sale with that. As with the X5690, which works on the version 2 Z400, there seem to be other unofficial processors that will work.... see HERE. Prices too high, versus eBay, but I'd assume they've proven all these can work. There is something special about the Z400 because most HP workstations have a microcode built into BIOS that prevents that.
Now.... what about cost? Search for X5675 with Google, go to the Intel Ark result, go to the sSpec link on the left, and you'll find there is only 1 (SSSLBYL, which is a typo.... it is SLYBL for the X5675). Search eBay for SLYBL, and you'll find one costs about 80.00 USD. You generally don't want to buy from China for this type of purchase..... go with a good US seller with good reputation. That is a good price. You can see my x5690 cost this way.... the Apple folks like this one too, so it drives up the price. Maybe take a look at a X5680.....