The original text is very good and mostly correct. Here is the checked and slightly improved version:
"During the day, the forest is full of bird chirping. A giant moose is munching on green grass, and little squirrels are busy looking for pine cones. At night, the forest changes. A lynx is out hunting, and frogs begin their croaky concert."
This text is grammatically correct and clear for a 5-year-old to understand. The sentence structure is simple and the words are appropriate. One tiny suggestion is to say "birdsong" instead of "bird chirping," because the word "chirping" is usually a verb, but the phrase "bird chirping" is still okay for children.
So, an alternative could be: "During the day, the forest is full of birds singing. A giant moose is munching on green grass, and little squirrels are busy looking for pine cones. At night, the forest changes. A lynx is out hunting, and frogs begin their croaky concert."