I caught my boyfriend in a lie, should I dump him?

My bf and I have been in a committed relationship for about 5 months. I decided I wanted to test his faithfulness so I asked my girlfriend who he doesn't know to add him on facebook. She sent him a couple flirty emails & gave him her yahoo messenger info so they could chat. He was a little flirty back with her in the emails, but pretty innocent overall. Well, he added her to his messenger the other night. So last night after we got off the phone, he logged onto messenger & started chatting with her. It was a pretty innocent chat, but when she asked him if he had a gf he said yes, but that we've been having some problems which is sort of true in the past, but we weren't having any lately. So I called him during the time he was chatting with her and he didn't answer his phone. I sent him an email on FB which he didn't reply to, but he did reply to an email my friend had sent him earlier. When I asked him about when I called him last night, he had told me that had gone to bed early & didn't hear his phone which was a lie because he was chatting. And then I asked him about the email I sent him on FB, he said he hadn't logged into FB all day so he didn't get it which was also a lie because he responded to my friend's email. So just curious what everyone makes of this? Should I dump him because he's a liar or am I being too harsh about this?