Let's start with the weight figures. The tested weight for the BMW F82 M4 is 3560 pounds. This is multiple sources now weighing the M4 in the 35XX pound range. The RS5 is the much heavier car at 3941 pounds.
The RS5's quoted horsepower figure at 450 does not mean anything as BMW's quoted 425 horsepower figure is much more in the real world. The difference between these cars is really about 100 horsepower and quite a bit of torque. The Audi with more weight, less power, and less torque is is simply overmatched.
This shows in the acceleration figures where the M4 trounces the RS5. Even though the RS5 has Quattro the M4 gets to 60 a tenth quicker at 4.2 seconds. The difference by 200 km/h (124 miles per hour) is a 1.6 seconds. The M4 is simply showing the RS5 its taillights past 60.
Around the track the RS5 gets a beatdown as well. It laps their test circuit in 1:41.5. The M4 is 2.6 seconds quicker at 1:38.9. The slalom is also in the M4's favor at 70.8 km/h to the RS5 67.5 km/h.
The M4 also has cleaner emissions and a lower price. Even its interior ergonomics are chosen over Audi which is the area Audi is traditionally praised over BMW.
What more is there to say? The M4 is on another level compared to any RS4 or RS5 model in Audi's current lineup. Audi needs a new car with more changes than just some new headlights.