If the correlation coefficient between X and Y is 0.7, then the correlation coefficient between U and V, where U = X - 5 and V = Y + 2, is: 

Key Points 

The correlation coefficient, denoted by r, quantifies the linear relationship between two random variables. It is formally defined as the covariance between the two variables divided by the product of their standard deviations. 
\(r = {Cov(X, Y) \over σ_X σ_Y}\); where, Cov(X, Y) denotes the covariance between X and Y, σ_X denotes the standard deviation of X, and σ_Y denotes the standard deviation of Y.

Let's denote the correlation between X and Y as r_XY. Therefore, \(r_{XY} = {Cov(X, Y) \over σ_X σ_Y}\)
Now, considering the transformations U = X - 5 and V = Y + 2, we need to find the correlation coefficient between U and V, denoted by \(r_{UV}\)
Given the properties of covariance and variance under linear transformation, we have:
Cov(U, V) = Cov(X - 5, Y + 2) = Cov(X, Y)

σ_U = σ_X (since the variance and hence the standard deviation do not change with shifts)
σ_V = σ_Y (since the variance and hence the standard deviation do not change with shifts)

Then, substituting these into the formula for r_UV, we have: \(r_{UV} = {Cov(U, V)\over σ_U σ_V} = {Cov(X, Y) \over σ_X σ_Y} = r_{XY}\) 

In conclusion, a linear transformation that consists of adding or subtracting a constant from a random variable does not affect the correlation coefficient between two variables. Thus, if the correlation coefficient between X and Y is 0.7, the correlation coefficient between U = X - 5 and V = Y + 2 remains 0.7.