after he had (ran,run)about 5 kilo, he had (sank,sunk) to the ground
You are working with the Past Perfect verb tense in that sentence. Check the
site below.
http://www.englishpage.com/verbpage/pastperfect.html
This site will give you a summary of all forms of verb tenses.
http://leo.stcloudstate.edu/grammar/tenses.html
To determine which verb form to use, we need to identify if the verb is in the past tense or past participle form.
In this case, the verb "had" indicates past tense, so we need to use the past tense form of the verbs "run" and "sink."
The correct forms would be:
"After he had run about 5 kilos, he had sunk to the ground."