When Does the Second Film "Planet of the Apes" (2001) Take Place?

"Planet of the Apes" is a science fiction film written by William Broyles Jr. with Lawrence Konner and Mark Rosenthal [adapting "La Planète des singes" (1963) by Pierre Boulle] and released July 27th, 2001. 

It takes place on an alternate timeline of the fictional Planet of the Apes universe in the year: 

5021 AD 

We know this because although a specific year is not mentioned in the film, we know it is later than 2029 AD and an adaptation offers an option. 

As Captain Leo Davidson falls into a time warp through an electromagnetic storm, we can see a chronometer read at least “24 11 2472” but the digital counter is still changing rapidly. A final arrival date is not shown. Nor is a departure date shown, later in the film, when a reverse trip through the electromagnetic storm is attempted. Though, this time, the chronometer is shown again counting backwards from at most “21 8 2682” but the digital counter does not appear to have started then. 

The novel adaptation (novelization) of the film DOES name a year setting: 5021 AD. Assuming a close adaptation, this is the best year we can ascertain for the main action of this story. 

Additionally, the film's prologue (before the first electromagnetic storm trip) is clearly set in 2029 AD. The second scene of the prologue includes a place and time setting title card that reads, "USAF Oberon Space Research Station 2029". Presumably, this is also the time setting of the final scene of the film although that scene is intentionally unclear in many ways.