Is it at all possible to turn a low res image of 3" x 5" inches to a high res image of 32" x 81" inches?
No, it is not possible.
Assuming that your image is a raster and not a vector.
If it were a vector, it can be scaled indefinitely.
Wow, that's asking for a miracle. If you consider that your low rez image of 3 x 5 at 75 dots per inch creates an image of 225 pixels by 375 pixels, you have very little with which to work.
Increasing the resolution to 300 dpi gives you 900 dots by 1500, which is not yet close to a low grade digital camera. Let's consider that you've started with 300 dpi.
Crank that up to 32x81 inches. That converts to about 28 dots per inch. You can find rulers with 1/32 inch markings and 28 dpi would be larger than the spacing of those markings.
On the other hand, you aren't likely to be looking at a 32 inch wide print so closely that you'll see such level of detail.
This does require that your original image begin at 300 dpi. Any number lower than that means all of the above math gets worse.
Some graphics programs will perform interpolation and/or dithering when enlarging a low resolution image. This will improve the results over raw expansion of the image.