Switching from your current tyre to an all-season tyre such as Michelin CrossClimate may improve ride quality to a degree, but it is important to note that the tyre type is just one factor that will affect ride comfort and changing to an all-season tyre will potentially bring with it other compromises. Your current Continental tyres are a summer tyre designed for high performance, whereas the CrossClimate has a design that will offer more deflection over bumps which should improve the ride, although the trade-off is that you will likely have slightly less overall grip, and potentially a small increase in road noise and fuel consumption. As your Q5 is an S-Line it is likely riding on sports suspension, and the 19-inch wheel is relatively large with a small aspect ratio which limits the amount of sidewall available to absorb bumps.

You may wish to consider switching to an 18-inch alloy wheels, which come with a 60 profile tyre rather than the 50 or 55 profile of your 19-inch wheels and would also allow you to choose a summer or all-season tyre while still improving the ride quality.