In theory, any MXM 2 video card will work. As with their bigger cousins, PCIe, any card will work if it's compatible with the slot. The caveat of course is the voltages, but with the older cards they were designed to get all they need directly from the slot (unlike the power hungry monsters today that need direct feeding from the PSU).
The other consideration is the heatsink mount. Nvidia and ATI/AMD typically don't use the same orientations of their heatsinks or screw holes so you would likely limited to the AMD family. However, that all goes out the window with laptop cards and they use the same orientation. Compare the video card from a 5720 to the 5920, yours is the ati, the 5920 can come with an nvidia 1GB card.
If you want to experiment, there are plenty of cheap options on eBay to try just to see if a different card would work at all. Honestly, I wouldn't bother and go straight for the card you want to upgrade to.
To be absolutely sure, you would need to contact Acer support for the supported voltages in the MXM slot. You would also need to contact AMD/nVidia for the voltages required by the card you're investigating.