60 km/h is 1 km/minute. 70 km/h is 6/7 km/min.
Suppose the party starts at 8 o'clock. So Lexi arrived at 8:05.
If D is the distance to the party then yesterday it took Lexi D minutes to get there travelling at 1 km/min.
Today it took her only 6D/7 minutes, and she arrived at 7:54.
D-5=6D/7+6 means that in terms of time, yesterday's time (reduced by 5 minutes because she was late) to get to the party is equivalent today's time (extended by 6 minutes because she was early). Another way of looking at this is the difference in arrival times is 11 minutes which is the result of the difference in speeds.
So D/7=11 min and D=77km.
CHECK
Time taken yesterday to get to the party was 77 min. That means, since Lexi arrived at 8:05 she must have left home 77 min earlier at 6:48. Time taken today was only 66 min, so 66 min before 7:54 is 6:48, the same time she left yesterday. This confirms that the distance between Lexi's home and the party house is 77 km. (The time of the party is irrelevant. The difference in arrival times is all that matters. If the party started at 8:05, for example, Lexi would have arrived exactly on time yesterday and would have been 11 minutes early today. She would still have left home at the same time each day.)