Jamieson, Fausset and Brown on 1 Thessalonians 3:5

5. For this cause--Because I know of your "tribulation" having actually begun (1Th 3:4).

when I--Greek, "when I also (as well as Timothy, who, Paul delicately implies, was equally anxious respecting them, compare "we," 1Th 3:1), could no longer contain myself (endure the suspense)."

I sent--Paul was the actual sender; hence the "I" here: Paul, Silas, and Timothy himself had agreed on the mission already, before Paul went to Athens: hence the "we," (see on 1Th 3:1).

to know--to learn the state of your faith, whether it stood the trial (Col 4:8).

lest ... have tempted ... and ... be--The indicative is used in the former sentence, the subjunctive in the latter. Translate therefore, "To know ... whether haply the tempter have tempted you (the indicative implying that he supposed such was the case), and lest (in that case) our labor may prove to be in vain" (compare Ga 4:11). Our labor in preaching would in that case be vain, so far as ye are concerned, but not as concerns us in so far as we have sincerely labored (Is 49:4; 1Co 3:8).