Barb, this is a tough one....and the child is still a little one (she's only 5, right?) Kids that age have a tough time telling a lie from the truth. Sometimes they lie to get out of trouble, and other times they lie because they are living in a fantasy world and tell what they WISH things were instead of how they really are.
If she's lying to get out of trouble for something, she may need to see that she will get punished twice. Once for what she did wrong and once for lying. BUT she should also know that if she does wrong, and tells the truth, that you'll go (a little) easier on her. She needs to learn at this point that she CAN tell the truth and you'll still love her.
I'm sure she is still struggling with the whole thing with her mom. Her life has been very unstable. She is here, there, she does not know from one day to the next what to expect--and she is developing her own little survival skill to protect herself. She NEEDS stability and love and consistency. She gets it with you, and then Mom takes it away. How hard must that be, when you are 5?