Welcome to the FCF
There is a break in C5 between 2004 when the faclifted C5II was launched, this had two new diesel engines (1.6HDi and 2.0HDi 138bhp - very good!). So im unsure if the 6 speed 2004 model you are talking about is a C5I or C5II and either 2.0HDi 138 or 2.2Hi 136. The 2.2 seems to have the most problems of the lot and so far I have avoided ownership of those, I found my 2.0HDi 138 superb, good economy and torque from a refined diesel engine.
Do check the dual mass flywheel is not making awful noises and the clutch is not slipping during peak torque. Every C5 diesel has a DMF and they are known to fail. I replaced mine at 25,000 miles, despite the clutch plate being like new (replaced anyway) but our other 2.0HDi 138 C5 is making horrible noises from the clutch now at 97,000 miles. Its not a cheap job.
Check all of the electrics, check for odd things like the indicators flashing a few times before they stop and the headlihts come on. This is a problem with the comms2000 unit.
If your going for anything other than the earlier 2.0HDi 110 8v (brilliant engine) then they all have diesel particulate filters. Not often a problem really but they dont like the car doing constant town use. They will eventually need the fluid topping up and the DPF filter replacing/cleaning, its expensive to replace it. This is why I have avoided the 2.2 as it was one of the first diesel engines to have a DPF and the 1.6 and 2.0HDi 138s are more refined in that area.
If its a 1.6 you stumble upon make sure it has been serviced every 10-12K miles at most and with the correct low sulphur oil - hard to tell I know. If left for long periods this can bring on turbo failure with this engine.
Suspension is a strong point on the C5s, it should ride softly-ish but not bouncy - if its bouncy the spheres are getting on a bit. Rattling will be front drops links - quite common.
Rear brake claipers can wedge out due to corrosion and wear the pads badly and odly, in extreme cases with C5s with small wheels the caliper meets the inside of the wheel rim. Also front calipers can have sticky handbrake arms, not always obvious to spot until a very noticeable wheel wobble develops and you cant see for smoke
Despite this I think of C5s as good and reliable cars which are stupidly good value for money too. When you look around at most more modern cars everything has a list as long as your arm of potential failures. We have had 5 C5s and I've covered just about ever common fault now, bar the DPF.
Find a good one which has been looked after and it should prove to be a reliable car. Our current two are 2002 C5 2.0HDi 110 SX hatch with 150K miles and a 2005 2.0HDi 138 VTR estate with 97K miles. Neither have been problematic to own for the last 3-4 years.
Good luck with your search
