For 1, ∠1 and ∠5 are supplementary is a given, so you can just write 'Given'
For 2, due to that 1 and 2 are vertical angles (angles that are opposite to each other when two lines cross according to Math is Fun)
For 3, since ∠1=∠2, ∠1 can be substituted by ∠2 in ∠1+∠5=180 to get ∠2+∠5=180. Therefore, they are supplementary.
For 4, due to that we have Consecutive Interior Angles (they are angles that are on one side of a transversal, which is the line that cuts through a and b,but inside the two lines according to Math is Fun) adding up to 180 degrees, a || b
Feel free to ask if you have any questions!