"My daughter(age 5) is having an infection in the pre-molar tooth. Dentist has advised to remove it. Is that normal?"
If your daughter is 5, the tooth is probably a baby or deciduous tooth.
If it is fractured, grossly decayed or abscessed, it may require removal. It should be assessed for space maintaining as early removal may lead to space loss for the permanent teeth possibly leadsing to orthodontic treatment.
Another ideas about "Remove pre-molar tooth" :
"It's probably a damaged baby molar. The best space maintainer is a baby tooth. If it can be saved (pulp treatment & stainless steel crown) consider that as first option. If tooth must be removed, imperative that space maintainer placed to prevent drifting of adjacent teeth causing a space problem."