The fact that Leslie and Corey are brother and sister is irrelevant information. Let us start by assigning variables to the values we are trying to find, Leslie's and Corey's ages:

L = Leslie's age

C = Corey's age

Leslie is 5 years older than Corey. This means that if we have Corey's age and add 5, then we get Leslie's age. We can express this mathematically as:

L = C + 5 (Equation 1)

We also know that the sum of Leslie's and Corey's ages is 51. This can be expressed mathematically as:

L + C = 51 (Equation 2)

We now have two equations (Equation 1 and Equation 2) and two unknowns (L and C). We can use substitution to solve for both unknowns.

We know that L = C + 5 from Equation 1. Substitute this for L in Equation 2 to get:

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(C+5) + C = 51

Rearranging terms, we can also express this as:

C + C + 5 = 51

Combining variables, we get:

2C + 5 = 51

Subtract 5 from both sides of the equation to isolate C:

2C + 5 - 5 = 51 - 5

2C = 46

Now divide both sides by 2:

2C/2 = 46/2

C = 23

Now that we have solved for Corey's age, we can use Equation 1 to determine Leslie's:

L = C + 5

L = 23 + 5 = 28

Therefore, Leslie is 28 and Corey is 23.

A quick double-check confirms that Leslies is 5 years older than Corey (28 - 5 = 23) and that the sum of the ages is 51 (28 + 23 = 51).

** Answer: Leslie is 28 years old and Corey is 23 years old. **