My DD, also 5, has been sort of going through this also, but mostly about her Daddy!

They will be playing and he will accidently knock her on the arm or something silly and she will come up and go "Muuuuuum, Daddy hit me...etc etc" which I know is not the truth, because I saw the whole thing!
The best way we have found to deal with this is for me to say to her "You need to talk to Daddy about this not Mummy" and she usually then says "But, but, but" and I am then firm again, and say "This is not to do with Mummy, please talk to Daddy about it", in which case she realises that there is no point. Since I have been really firm about it, she has stopped a lot.
I know when she is just being silly as opposed to when she actually has something serious and important to tell me -her tone of voice is really whiney, where if it is something that is seriously bothering her, she has a really quiet voice, and I know to take her seriously......and she knows Mummy will listen to her and take it seriously, and she knows she can tell me anything.

When she has done it about other children (if it is something silly like such and such took my toy etc etc), then I always tell her not to worry about what they are doing, you just need to make sure you are doing the right thing, and she generally just leaves it there.

I think that it is just an age thing really, and it makes them feel a bit important!

As for dishonesty, the few times she has tried to be dishonest, she has been found out, so she doesn't even bother trying anymore, and is honest even when she knows she might get into trouble!