Speaking from experience, our oldest boy loved the novelty of staying with his Nana for several days at that age. The idea of opening up a gift each day is really cool! He shouldn't see it as a buy-off unless experience has taught him to do so... not likely at his age, at least not in the world I know. Gestures like a gift-a-day that tell a kid that you thought of him often and with care. My kids always noticed the subtle touches and loved them -- and at five he's probably ready for little notes, as well. My mom used to hide creatively made little notes for me, sometimes in tiny handmade boxes or dangling in a pattern from the window. I still have them.
Videos are good, too. We made one for our oldest boy when we were gone once (he was six) and he loved it. We told him which places were really "boring" and then I'd hustle the camera over to try to "wake" Dad in the lecture hall. We got strangers to play along. We gave him 'behind the scenes' tours. We went into toy shops and filmed while Dad was chased by toy sharks until a giant octopus devoured the camera and we all "sunk" into the stuffed animal display. (God bless Disney... they're patient people, really.) Whatever we bought him, we'd film each other picking it out. We'd stand with our backs to the cool toys and 'argue' over which totally lame, inappropriate gift to get him... he'd watch the video with us later and be yelling at the TV, "No, Mom! Not the Barbie dress!" Then afterward we'd give him his real gifts; surprisingly good one, at that!
Also, try accentuating the differences a bit. Each of our kids loved "Only At Nana's" rules. For example, we don't allow sugary cereal in the house, meanies that we are. But Nana keeps a set of the tiny 'single-serving' boxes of popular cereals ... one for each breakfast of the visit. She'd make a point to ask us in front of the kids if we'd allow it... and we were always happy to. Only at Nana's could the kids get drug round the hardwood floors by their ankles while their bums 'polished' the 'dingy' floor. And Nana makes each kid a hot water bottle to sleep with -- they like it so much they even beg for it in summer. I kid you not. What seems dopey to us, often seems like the coolest thing in the world to a 5 year old.
Have a great trip! And congratulations to you and your daughter!