One week is forever, at her age. And as another poster noted, seeing them once a month sounds like "pretty often" to an adult but isn't to a kid. Has she even slept over at their house without you, ever, on these monthly visits? If not -- you can take her for a sleepover where you also stay, to get her used to the idea. But please don't force her to be away for an entire week when she is clearly telling it you it distresses her. Also, it likely won't be a week, because after one or two or three days, you will get the call from the grandparents that she needs to come home -- and that call might come in the middle of the night.
You want their home to be a place of positive associations for her. But if you force her to go, then the next time your whole family visits, she will be more apprehensive, more afraid, and might even worry that -- though she's going WITH you -- that you intend to leave her at the grandparents' house like you did "last time." You really don't want to deal with the repairs and reassurances you'll have to do to make her comfortable there on later visits if you force her to stay there a week.
I am not keen on the idea someone suggested of going for a weekend and telling her you'll pack thiings so she can stay on for a week if she wants to extend the visit. I think that puts too much responsibility on a child this young; she would be in the position of hearing from you over the phone, "So do you want to stay the rest of the week?" while the grandparents are nodding yes next to her. Too much pressure on a small kid to decide (and she could say yes that moment, then change her mind five minutes later). Set a definite time limit, overnight or two nights, and then pick her up when you say you will -- that way she knows you WILL always come get her when you say you will, and her confidence at being separated from you will grow because she knows she can rely on you to start and end her visits when you say you will (and won't put it on her shoulders).
Also, are the grandparents really fully aware of what it's like to have a five-year-old in their home, 24/7, for a full week? Maybe they do this with other grandkids and it's dandy and they have the full arsenal of energy and activities ready, but if not -- they will realize they took on too much, perhaps. She might wander at night, call out, have dreams, want food and drink not on their schedule, say she's bored, not like the activities they have planned, etc. -- are they up for all that and ready to switch gears to keep the visit positive?