Race Comment Explainer

Original comment with matches highlighted:

off the pace in last pair, pushed along in modest 5th ly, taile, soon quickly,

Matched phrases & meanings

Phrase	Meaning
Pushed along	The jockey started to urge the horse (hand-riding, not necessarily using the whip).
tailed off	A definitive statement that the horse was finished and effectively out of the race
home turn	This is the final bend or corner of the track, just before the horses enter the final straight run to the finish line.
Weakened	The horse lost speed and dropped back through the field.

Summary

The jockey started to urge the horse (hand-riding, not necessarily using the whip).
A definitive statement that the horse was finished and effectively out of the race
This is the final bend or corner of the track, just before the horses enter the final straight run to the finish line.
The horse lost speed and dropped back through the field.