Introduction:
Parikshit wants to form a cube using cuboids made of plasticine. He has cuboids with dimensions of 5 cm, 2 cm, and 5 cm. We need to determine how many such cuboids he will need to form a cube.

Understanding the problem:
To solve this problem, we need to calculate the volume of each cuboid and the volume of the cube that Parikshit wants to create. Then we can divide the volume of the cube by the volume of a single cuboid to find out how many cuboids are needed.

Calculating the volume of a cuboid:
The volume of a cuboid is calculated by multiplying its length, width, and height. In this case, the dimensions of the cuboid are given as 5 cm, 2 cm, and 5 cm. So, the volume of a single cuboid can be calculated as follows:

Volume of a cuboid = Length × Width × Height
= 5 cm × 2 cm × 5 cm
= 50 cm³

Calculating the volume of the cube:
To calculate the volume of the cube, we need to determine the length of its sides. Since a cube has equal sides, we can choose any one of the dimensions provided for the cuboid. In this case, the side length of the cube will be 5 cm. So, the volume of the cube can be calculated as follows:

Volume of the cube = Side length × Side length × Side length
= 5 cm × 5 cm × 5 cm
= 125 cm³

Determining the number of cuboids needed:
Now that we have the volume of a single cuboid (50 cm³) and the volume of the cube (125 cm³), we can divide the volume of the cube by the volume of a single cuboid to find out how many cuboids are needed.

Number of cuboids needed = Volume of the cube / Volume of a single cuboid
= 125 cm³ / 50 cm³
= 2.5

Since we cannot have a fraction of a cuboid, we need to round up the number to the nearest whole number. Therefore, Parikshit will need 3 such cuboids to form a cube.

Conclusion:
Parikshit will need 3 cuboids with dimensions of 5 cm, 2 cm, and 5 cm to form a cube.