Final answer:
Levofloxacin is the best antibiotic for treating sinusitis with suspected gram-negative organisms, as it has broad-spectrum activity including coverage against many gram-negative bacteria.
Step-by-step explanation:
When treating acute or chronic sinusitis where gram-negative organisms are suspected, levofloxacin is considered the best option among the provided antibiotics. Penicillins like penicillin V and amoxicillin are generally effective against many gram-positive bacteria and some gram-negative bacteria such as E. coli, but they may not provide the broadest coverage for gram-negative organisms implicated in sinusitis. Clindamycin is primarily used for anaerobic infections and certain gram-positive cocci but is less effective against gram-negative bacteria. Levofloxacin, a fluoroquinolone antibiotic, has broad-spectrum activity that includes excellent coverage against many gram-negative organisms and is considered effective for respiratory tract infections, including those caused by drug-resistant strains of bacteria.