This is the worst. You cant try to logic but thats not always helpful with a 5 year old and Im sure already been tried. What if she can give it to herself (under supervision of course). Telling her she can give it to herself via the syringe and even dose it out so that she feels in control of the situation. Maybe ask her for ideas on how she might be willing to take it and then see if that works. It also can reinforce that she is control of her own body but as her parent you have to ensure she is safe and well so if she won't do it herself you have to step in. I don't know. Its a hard one. Please keep us informed on anything that you find that works!