sid (unstable): 5.3.9-2
buster (testing): 4.19.67-2+deb10u2
stretch (stable): 4.9.189-3+deb9u2
jessie (oldstable): 3.16.76-1

Debian GNU/Linux device driver check & report

HP: dc5750

PCI IDWorks?VendorDeviceDriverKernel
10025950ATI Technologies IncRS480 Host Bridge
10025a3fATI Technologies IncRS480 PCI Bridge
10025a39ATI Technologies IncRS480 PCI Bridge
10024380YesATI Technologies IncSB600 Non-Raid-5 SATAahciv2.6.25-
10024387ATI Technologies IncSB600 USB (OHCI0)
10024388ATI Technologies IncSB600 USB (OHCI1)
10024389ATI Technologies IncSB600 USB (OHCI2)
1002438aATI Technologies IncSB600 USB (OHCI3)
1002438bATI Technologies IncSB600 USB (OHCI4)
10024386ATI Technologies IncSB600 USB Controller (EHCI)
10024385YesATI Technologies IncSBx00 SMBus Controlleri2c-piix4v2.6.25-
1002438cYesATI Technologies IncSB600 IDEpata_atiixpv2.6.25-
10024383YesATI Technologies IncSBx00 Azalia (Intel HDA)snd-hda-intelv2.6.25-
1002438dATI Technologies IncSB600 PCI to LPC Bridge
10024384ATI Technologies IncSBx00 PCI to PCI Bridge
10221100Advanced Micro Devices [AMD]K8 [Athlon64/Opteron] HyperTransport Technology Configuration
10221101Advanced Micro Devices [AMD]K8 [Athlon64/Opteron] Address Map
10221102Advanced Micro Devices [AMD]K8 [Athlon64/Opteron] DRAM Controller
10221103YesAdvanced Micro Devices [AMD]K8 [Athlon64/Opteron] Miscellaneous Controlk8tempv2.6.25-
10025974YesATI Technologies IncRS482 [Radeon Xpress 200]radeonv2.6.35-
10025874ATI Technologies IncRadeon Xpress Series (RS482)
105a4d69YesPromise Technology, Inc.20269pata_pdc2027xv2.6.25-
10953512YesSilicon Image, Inc.SiI 3512 [SATALink/SATARaid] Serial ATA Controllersata_silv2.6.25-
14e4167bYesBroadcom CorporationNetXtreme BCM5755 Gigabit Ethernet PCI Expresstg3v2.6.25-

Using either Ubuntu Feisty 7.04, or FC6:
smbus has no driver.  lm-sensors fails.
Bug in SB600 SATA controller: kernel loops at boot, when HP Lightscribe  DVD drive ('HL-DT-ST' 'DVD+-RW GSA-H31L' 'W616' Removable CD-ROM according to cdrecord -scanbus) is plugged into it.  (I added Rosewill FC-210 sata_sil PCI card and plugged DVD into it, to avoid this bug.)  Various ATI graphics problems, dual head barely limping w/open source driver.