the line of best fit is r = beta + e(r cos phi)
That suggests you define x_i = r cos phi and y_i = r (i=1,..,5).
The formulae for least squares are this:
beta = (sum x_i y_i times sum x_i - sum y_i times sum x_i^2) / ((sum x_i)^2 - n sum x_i^2) --- here n = 5
e = (sum y_i - n beta) / sum x_i
beta = 1.451 and e = 0.811 (i.e. elliptic)
If phi = 4.6, then your formula for r yields r = 1.33.