Given angle theta = 45^.

The slope $m$ of a line is given by the tangent of the angle $\theta$ it makes with the positive x-axis.
Given angle $\theta = 45^\circ$.

$$m = \tan(\theta)$$ $$m = \tan(45^\circ)$$ $$m = 1$$

The problem states that the line cuts 5 units on the positive part of the Y-axis. This means the y-intercept $c$ is 5.

$$c = 5$$

Using the slope-intercept form of a linear equation, $y = mx + c$, substitute the values of $m$ and $c$.

$$y = (1)x + 5$$ $$y = x + 5$$