My daughter(age 5) is having an infection in the pre-molar tooth. dentist has advised to remove it. is that normal?

Depends on reason: 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.

Try to save tooth: The only reason it should be removed is if the decay is so extensive that it cannot be restored. Pulp treatment and a stainless steel crown can often save a baby tooth that otherwise would be lost.

Try to save: Your daughter is 4-5 years from eruption of her permanent premolars. 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.

That depends: Given her age, this is most likely a baby molar not a pre-molar. These teeth ideally need to stay in till between 8 /12 ; 14 years of age, depending on which tooth it is. Ideally the tooth should be saved if possible, however if the infection is too bad or your child's behavior will not allow restoration then extraction is indicated. A pediatric dentist can help guild you to the correct choice.