Hm, that is strange. The ICAO recommended wake separations are 4 miles for a Heavy behind Heavy on approach/take-off, 5 miles for cruise – only 25 % bigger. For a Heavy behind Ai-380, it is 10 miles for approach/take-off, 15 miles for cruise – only 50 % bigger. Whereas the cruise speed, at about 0,85 Mach or 500 knots TAS, is at least 200 % greater than the speeds on approach/take-off (around 150 knots…). So a plane at a minimum safe distance behind a craft cruising ahead is leaving at most a half, and likely one-third, the time for wake decay that is allowed on approach/take-off.

How do the separation requirements change from 4 miles takeoff limit to 5 miles cruise limit over the course of the climb?

And that is reasonable, because wake intensity is not constant. It decreases with airspeed and configuration, so that the wake of a cruising aircraft is considerably lower amplitude than that of a approaching aircraft with similar weight. Same with sensitivity: At cruise speed a wake would induce lower forces than at approach or take-off speed (same vortex strength, same aircraft, same configuration). Additionally, any turbulence or even upset is far less dangerous in cruise as ground clearance is suffcient to counteract and small deviations from planned flight-path is less of concern.