Introduction:
In this question, we are given that the population of a place increased to 50,000 in 2003 at a rate of 5% per annum. We are required to find the population in 2001 and 2005.

Given:
- Population in 2003 = 50,000
- Rate of increase = 5% per annum

Calculating the population in 2001:
To find the population in 2001, we need to calculate the population growth from 2001 to 2003.

Step 1: Calculate the growth rate per year.
The growth rate per year is given as 5%. We can calculate the growth rate per year as follows:
Growth rate per year = (5/100) = 0.05

Step 2: Calculate the total growth from 2001 to 2003.
To calculate the total growth from 2001 to 2003, we need to multiply the growth rate per year by the number of years.
Total growth = Growth rate per year * Number of years
Total growth = 0.05 * 2 (since there are 2 years from 2001 to 2003)
Total growth = 0.1

Step 3: Calculate the population in 2001.
The population in 2001 can be calculated by subtracting the total growth from the population in 2003.
Population in 2001 = Population in 2003 - Total growth
Population in 2001 = 50,000 - 0.1
Population in 2001 = 49,999.9 (approximately)

Therefore, the population in 2001 is approximately 49,999.9.

Calculating the population in 2005:
To find the population in 2005, we need to calculate the population growth from 2003 to 2005.

Step 1: Calculate the growth rate per year.
The growth rate per year is given as 5%. We can calculate the growth rate per year as follows:
Growth rate per year = (5/100) = 0.05

Step 2: Calculate the total growth from 2003 to 2005.
To calculate the total growth from 2003 to 2005, we need to multiply the growth rate per year by the number of years.
Total growth = Growth rate per year * Number of years
Total growth = 0.05 * 2 (since there are 2 years from 2003 to 2005)
Total growth = 0.1

Step 3: Calculate the population in 2005.
The population in 2005 can be calculated by adding the total growth to the population in 2003.
Population in 2005 = Population in 2003 + Total growth
Population in 2005 = 50,000 + 0.1
Population in 2005 = 50,000.1 (approximately)

Therefore, the population in 2005 is approximately 50,000.1.

Summary:
- The population in 2001 is approximately 49,999.9.
- The population in 2005 is approximately 50,000.1.