I think you definitely need the handwritten one, with the tears and the stains. For multiple reasons. Your character is in the handwritten one, you tears are in indicator of how hard it was and how much you loved her. Secondly, it's a question of protecting your loved ones. Handwritten notes show that you decided to commit suicide, that you planned it and carried it out, and not that someone killed you and placed a note next to you. I don't think they'll implicate a 5 year old, but you have other loved ones, too.
I had a lecture yesterday on suicide in my country by the police, they said that 99.5% of suicide cases get an autopsy, no matter what, to ensure that it was truly suicide and nothing else. They also mentioned handwritten notes are checked against other samples of handwriting found in your home, such as shopping lists or whatever they can get their hands on. So to protect your loved ones, write by hand, leave some shopping lists lying around as well.
I have done it for my will that I've handwritten it AND typed it, my handwriting isn't the best. For my loved ones.. well, they have to struggle through, they know my handwriting and so far they've always managed.
I wish you luck, and I do like the idea of the video, maybe at least one audio recording if you don't want to have visual? Maybe even something as mundane as going outside and .. I don't know, filming the dogs running around with you commenting in the background, just so she has the voice, something you are talking about to her. I know I'll be watching the videos my love send me of hotel rooms he has been to when I CTB. When he went abroad, he'd make video snippets of what the hotel room looks like, simply 'there's the bed, there's the tv, I'll be sleeping there and hey, they have a desk, let me show you one really cool thing they have in the bathroom...' And then he'd stand in front of a mirror, waving at me saying his and saying that he was okay and that he missed us. It's a random, weird video, but he is there, in it, I can see him, I can hear him, I can remember him. Maybe something like this would already be sufficient. You don't necessarily need to point the camera at you and read your words to her.