downsized to +- 5mp (like when you set a wallpaper on your pc it adjust to your screen resolution)
First, a 2560 x 1440 display is well under four megapickles, smaller even than you're indicating.
And, at such a low resolution, assuming good technique, there's not going to be a significant difference in sharpness regardless of the source.
You can get a feel for that in the images at the thread I posted to. The 100% crops from the 70-200 are noticeably softer than the 100% crops from the 400, but not overwhelmingly so. But, once the image gets scaled down to the whole frame picture, the only differences between the two are the depth of field.
You might want to play around with this for yourself. With a bit of Googling, you can find full-size images from practically any combination of lens and camera you might care to consider. Crop and scale as desired. (And be sure to perform suitable post-processing, especially sharpening, after modification!)
What you'll find is that the scenario you're describing is the second most forgiving one in all of modern photography, right after regular Web photography. And both are about as forgiving as old school newspaper photography, which is notoriously forgiving. You'll have to work hard to find something that doesn't excel at what you're describing.
Hell, even an iPhone would do a pretty good job. And, no, I'm not kidding. With good technique and good light, you could make a stunning full-desktop photo with an iPhone.