How can I tell my partner I'm asexual?

Sorry in advance for the long description.

I’m a 25 yr old female, and in a relationship with my girlfriend of 5 years. Growing up, I never seriously dated guys, the thought of it made me literally sick to my stomach. I would get along with them much better as friends but never had an attraction to them. I found that I was much more comfortable being around and being flirty/romantic with women. It was for this reason I eventually came out as gay. I have had a couple of relationships with women before my current girlfriend that were neither lengthy, nor very serious. I had been sexual with them, sometimes I really wanted to, and other times not at all – sometimes even thinking how much I was ready for it to be over – and that it seemed like something I was just supposed to do.

When I met my current girlfriend there was a pretty long period where we were very sexual. We have been together 5 years now and I have never been as happy as I am with her. The biggest problem in our relationship is that I never want to have sex. I rarely enjoy it, and I almost never think about it. Those feelings started to come on within the first year of our relationship and I wasn’t sure why, I love her very much, I care about her, and what I want to do most is make her happy. Believe it or not recently she was actually the one who suggested that I may be asexual. I told her that I didn’t know enough about it to even consider it, and was almost a little angry that she had suggested it. It wasn’t until recently that I actually read up on it, and I was blown away by how many similarities I shared with people writing on the subject. At first I was scared and nervous that this could actually be me, but then I began to feel almost relieved that this was a thing, and it could be the thing that explains why I feel the way I do.

I remember when she suggested it, I said something along the lines of “well if I am, then what?” and she said “I don’t know”. If I truly am asexual, how can I present this to her? I don’t want to lose my relationship. For me, the relationship has everything I want – my only frustrations are when she gets upset with me, but when shes upset with me it’s usually because she feels unloved because of MY actions. She has told me that our relationship is the whole package, except for the lack of sex/affection.

I don’t know how or when to approach her, and I’m not sure how she will react or what solution we will come up with (if any). I think I’m just looking for some support, or perhaps anyone else who is familiar with a similar situation?