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GentlePurpleRain
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The children are age 4aged $4$ and 1.
4$1$.

$4$ is the only number which can be a product of 2two different combinations of 2two numbers below 6$6$, whilewhere one of these combinations consists of 2two identical numbers.
We

We need 2two combinations because the information ofknowing the product of their ages wasn't enough information.
One

One of these combinations has to consist of 2two identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.
  

The only product this can refer to is 4$4$ with the combinations 22 and 14$2\times2$ and $1\times4$.

The children are age 4 and 1.
4 is the only number which can be a product of 2 different combinations of 2 numbers below 6, while one of these combinations consists of 2 identical numbers.
We need 2 combinations because the information of the product of their ages wasn't enough information.
One of these combinations has to consist of 2 identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.
 The only product this can refer to is 4 with the combinations 22 and 14.

The children are aged $4$ and $1$.

$4$ is the only number which can be a product of two different combinations of two numbers below $6$, where one of these combinations consists of two identical numbers.

We need two combinations because knowing the product of their ages wasn't enough information.

One of these combinations has to consist of two identical numbers because the information that there is one child that is older than the other one has to eliminate that combination. 

The only product this can refer to is $4$ with the combinations $2\times2$ and $1\times4$.

The children are age 4 and 1

4 is the only number which can be a product of 2 different combinations of 2 numbers below 6, while one of these combinations consists of 2 identical numbers.

We need 2 combinations because the information of the product of their ages wasnt enough information.

One of these combinations has to consist of 2 identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.

The only product this can refer to is 4 with the combinations 22 and 14.

The children are age 4 and 1.
4 is the only number which can be a product of 2 different combinations of 2 numbers below 6, while one of these combinations consists of 2 identical numbers.
We need 2 combinations because the information of the product of their ages wasn't enough information.
One of these combinations has to consist of 2 identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.
The only product this can refer to is 4 with the combinations 22 and 14.

The children are age 4 and 1

4 is the only number which can be a product of 2 different combinations of 2 numbers below 6, while one of these combinations consists of 2 identical numbers.

We need 2 combinations because the information of the product of their ages wasnt enough information.

One of these combinations has to consist of 2 identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.

The only product this can refer to is 4 with the combinations 22 and 14.

The children are age 4 and 1.
4 is the only number which can be a product of 2 different combinations of 2 numbers below 6, while one of these combinations consists of 2 identical numbers.
We need 2 combinations because the information of the product of their ages wasn't enough information.
One of these combinations has to consist of 2 identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.
The only product this can refer to is 4 with the combinations 22 and 14.

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The Dark Truth
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The children are age 4 and 1

4 is the only number which can be a product of 2 different combinations of 2 numbers below 6, while one of these combinations consists of 2 identical numbers.

We need 2 combinations because the information of the product of their ages wasnt enough information.

One of these combinations has to consist of 2 identical numbers because the information that there is one child that is older than the other one has to eliminate that combination.

The only product this can refer to is 4 with the combinations 22 and 14.