Use diodes to obtain lowered DC voltage?
First, why would you do this? The 7805 will be perfectly fine with 12V. If you're passing a lot of current, use a heatsink. The diodes will only move power loss from the regulator to the diodes themselves.


In this case it should be fine, but diodes do not drop a fixed voltage; the voltage drop varies depending on current in a non-linear fashion.

So for example getting 5V from a 12V source using 10 diodes in series would be bad, and the voltage could range from as much as 7V to as little as 2V, depending on the current draw. The 7805 has a minimum voltage of 7V to output 5V at 1 amp, so as long as you can guarantee this 7V you should be okay. 

Note that the output of the 7805 will vary depending on input voltage by a few millivolts - it will be slightly higher at 12V than at 7V.
The same loss happens no matter if you use resistors or diodes. The energy must go somewhere and it is converted into heat by either resistors or diodes.
The best practice here is just to feed 12V into the 7805. Introducing more components into the circuit will make for more chance of failure. 
Why is a heatsink not practical? Here, I'm unsure if potting would work. Best to ask someone else.


You should be cautious when using the 7805 in an automotive circuit. The battery line is a harsh place. When you turn the headlamp(s) on your car/bike off, for example, the excess energy in the alternator has to go somewhere and it does - it appears as up to a 60V spike on the 12V line. And in some rare circumstances you can get a negative voltage on the battery line. Both of these situations will destroy a 7805, and the output could short, connecting the battery line to the 5V output, giving your load 12V instead of 5V.