The AOA for minimum drag (i.e. best L/D) is not affected by flight path angle, so whether you are gliding, in level flight or climbing it will be the same. That translates to the same airspeed, for a given weight. 60 knots in this case according to Cessna, who should know these things.
You are confusing angle of attack, pitch angle and flight path angle. Assuming the wing incidence is zero:
Pitch Angle = Flight Path Angle + AOA
In level flight, flight path angle is zero so for minimum drag speed of 60 kts, which you assumed to be an AOA of 4 deg, pitch will also be 4 degrees. In a 5 degree glide at 4 degrees AOA, the pitch angle will be 1 degree nose down. A climb angle of 5 degrees with AOA of 4 deg means pitch angle will be 9 deg. In all three cases IAS will be 60, and the wing will be at maximum L/D. Only the power setting will be different.
Minimum drag speed is not usually the optimum cruising speed, however. You will stay aloft for a long time, but won't get very far. Cruising speeds are set higher so range is optimised.
In other words, aircraft are not designed to cruise at L/D max, but much faster.