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Sorry if this is repeating old information but I have never seen it reported before.
On my C5 both high beam and the drivers side low beam required a counterclockwise turn to remove the bulb from the headlamp. I was getting nowhere in replacing the low beam bulb on the passenger side until I remove the headlamp cover and could see that it would take a CLOCKWISE turn to remove the bulb.
Maybe my '98 C5 is the only one like this, but if you are having trouble with the passenger side low beam bulb removal, you might try giving it a clockwise twist.
PS: Actually it turned out to be a good thing that I removed the headlamp cover because I was able to see that the other bulbs that I thought were correctly installed did not have all of the tabs in place.
Bill
'98 coupe, white/oak
'91 ZR-1 #1768, turq/saddle (1of21)
Actually the owners manual has a nicely detailed set of instructions on how to change a light bulb. But to answer the question, remove the 3 phillips head screws on the sides of the black bezels and the bezel will slide off exposing more of the headlamp assenbly. You can also see the fog lamp fitting with the bezel removed.
While your at it, try a pair of the new Sylvania Silver Star bulbs. They operate at a light intensity of 4100 kevin (compared to the factory 3000 kevin) and are aa ultra white light. I did my low and high beams and I can see again at night! Auto Zone has them for $19.99 a bulb with a rebate of $10.00 on a pair. The lows are 9006 and the highs are 9005's.