Your link didn't work for me but I found the attached circuit muddling through the site. If this is the circuit it could be modified to work on 5 Volts but the first thing that is a problem is a 12 volt relay coil that likely will not work at all on 5 volts. You would need to sub a 5 volt coil relay and make sure that the transistor could drive it. Then change some resistor values maybe. The values of R3 & R4 would be reduced so the LEDs work.
Now the link works. I know the resistors for these 2 leds must be changed also the relay with a 5v coil but i don't know if the transistor can drive the relay.
The caps would be fine. You may need to play with R1 a little. R1 plus the pot plus the value (light & dark resistance) of the LDR determine when the transistor is turned on (saturated) to drive the relay. As long as you go with a relay coil that draws the same or less current than what is there it should work just fine.