The downloads listed below include various save points from each level, including most secrets and especially difficult points. Each file also includes a text document describing the location of each save. For a complete list of all 137 Chronicles saves, see here.
IMPORTANT: There are two sets of files for each level. One was made with the original, un-patched game, the other with the Multi Patch for Windows XP/Vista/7/8/10 from tombraiderchronicles.com. In my experience, most of the original game saves will load in the patched game, but if you're having any trouble, try the other version. The Multi-Patched saves should also work for the GOG and Steam downloads.
In a tight spot? Don't panic. Download a Tomb Raider savegame file.
Downloads for the individual levels are zip files ranging from 8 to 19 KB in size.
Russian Submarine Levels
Level 4: The Base (original game | multi-patched version)
Level 5: The Submarine (original game | multi-patched version)
Level 6: Deepsea Dive (original game | multi-patched version)
Level 7: Sinking Sub (original game | multi-patched version)
VCI Headquarters Levels
Special thanks to Eldin and Luka for the Windows XP/Vista/7 saves.
Additional Chronicles PC Saves
Jeff Reid's Complete TR Chronicles PC Saves (145 KB zip file) - Jeff has provided another set of TR5 saves in case I don't have the exact point you need. The download includes a text document detailing where each save was made.