Each new step in science (blank) twenty seemingly (blank) facts as merely the various manifestations of a single principle.

1-unifies...harmonious
2-reconciles...discordant
3-integrates...identical
4-undermines...erroneous
5-illuminates...consistent

Each new step in science reconciles twenty seemingly discordant facts as merely the various  manifestations of a single principle.

Explanation:

Even though the only context we have is the sentence itself, we can safely choose number 2. This type of sentence is used when we wish to present contrasting ideas. There would be no reason, for example, for science to unify what is already harmonious, or to undermine what is already erroneous. Those ideas are redundant. It makes much more sense to say that science reconciles facts that are seemingly discordant. That is the wonder in science: to see different things as the manifestations of a single principle, which could seem, if science did not exist, impossible.

the pronoun reference replaces a noun, but you have to make sure there's no room for confusion.

in the first sentence "her" could be referring to shely or to the sister. the answer there is "shelly called her sister and told her about the new baby."

in the second sentence "it" could be referring to the roof or the floor. the answer there is "since the roof leaks on the family room floor, we need to repair the roof."

where is the