Hi Vishwa. Page 18 of the manual for the 5840 says, "Be sure to connect your video source components in the same way you connect your video monitor to HTR-5840." Whereas, for the 5850, you do the same thing if Video Conversion is set to off. Which means, I think, that this receiver does not have video upconversion. This would mean that each source (DVD & VCR) would have to have its separate connections to the TV.
You've got your DVD to receiver to TV via S-cables. You'll have to hook up your VCR to receiver to TV via composite cables. That is, yellow composite from VCR to receiver (the VCR In spot) and another yellow composite from receiver (either the VCR out spot or the Monitor Out spot, below the VCR section) to TV.
I could be wrong about this, so try it out and see if that works. If not, there are far more knowledgeable people than I on this forum who can help you out. Good luck!
cheers,
supervij
EDIT: AVRat, ya beat to it!