If you observe carefully, you will notice that within a time span of seven years (from "five years ago" to "in two years time"), Jane's mother would go from "4 times as old as Jane" to "3 times as old as Jane".

Remember that age differences do not actually change at all.

Let the mother's age five years ago be 4 units and Jane's age be 1 unit. Their age difference is...

3 units.

Let the mother's age two years later be 3 parts and Jane's age be 1 part (do not use "unit" here). Their age difference is...

2 parts.

Because they grow old together, their age differences will never change (unless you defy the rules of time by going back in time somehow).

So, 3 units will have the same value as 2 parts, i.e.

2 parts = 3 units
1 part = 3/2 = 1.5 units

Jane's age two years later is 1 part, or 1.5 units. Jane's age five years ago was 1 unit. This is a difference of 0.5 unit, in a time span of 7 years. So...

0.5 unit = 7 years
1/2 unit = 7 years
1 unit = 14 years

So, Jane's age five years ago was 14.
The mother's age five years ago was 4 units, or 56.

The mother's current age is 56 + 5, or 61.

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Check.

Now:
Mother's age is 61
Jane's age is 19

Five years ago:
Mother's age was 56.
Jane's age was 14.
Mother is 4 times as old as Jane.

Two years later:
Mother's age is 63.
Jane's age is 21.
Mother is 3 times as old as Jane.