Does adding antibiotic after 5-10 mins of innoculation affect the protein yield or growth?
That is not true. If you had forgotten to add the antibiotic before inoculation then you can add it before the bacteria starts growing. Make sure you add it when the bacteria is still in lag phase. If you add it later then it won't be effective as some non-resistant (non-transformed) bacteria would have already expanded their population. Ampicillin and kanamycin are best effective when the bacteria are growing. Even though these antibiotics are considered bacteriocidal, you would end up having unnecessary biomass in your culture.

So 5min delay for E.coli is not an issue. (I think this happens to all of us: forgetting to add antibiotic).