Stockholm is a beautiful city with a lot to offer. Here's an ideal itinerary for 5 days in Stockholm:

Day 1: Arrival and Old Town Exploration

• Arrive in Stockholm and check into your hotel
• Head to Gamla Stan, the old town of Stockholm, and explore the narrow streets and colorful buildings
• Visit the Royal Palace and the Stockholm Cathedral
• Have lunch at one of the many cozy cafes in the area
• Take a boat tour around the archipelago to see the city from the water
• Enjoy dinner at a traditional Swedish restaurant in Gamla Stan

Day 2: Museums and Parks

• Start the day with a visit to the Vasa Museum, which houses a 17th-century warship that sank on its maiden voyage
• Head to the Skansen Open-Air Museum to learn about Swedish history and culture
• Have lunch at one of the many food stalls in the park
• Visit the ABBA Museum to learn about the famous Swedish pop group
• Take a stroll through the beautiful Djurgarden Park
• Enjoy dinner at a trendy restaurant in the Sodermalm neighborhood

Day 3: Shopping and Sightseeing

• Start the day with a visit to the Stockholm City Hall, where the Nobel Prize banquet is held
• Head to the trendy shopping district of Ostermalm and browse the high-end boutiques and designer stores
• Have lunch at one of the many cafes in the area
• Visit the Fotografiska Museum to see contemporary photography exhibitions
• Take a walk along the waterfront and enjoy the views of the city
• Enjoy dinner at a cozy restaurant in the Vasastan neighborhood

Day 4: Island Hopping

• Take a ferry to the island of Fjaderholmarna and explore the quaint village and artisan shops
• Have lunch at one of the seafood restaurants on the island
• Take a ferry to the island of Djurgarden and visit the ABBA Museum or the Skansen Open-Air Museum
• Take a stroll through the beautiful gardens of Rosendals Tradgard
• Enjoy dinner at a restaurant with a view of the water

Day 5: Modern Art and Nightlife

• Start the day with a visit to the Moderna Museet to see contemporary art exhibitions
• Head to the trendy neighborhood of SoFo and browse the vintage shops and art galleries
• Have lunch at one of the many hip cafes in the area
• Take a walk through the colorful streets of the Sodermalm neighborhood
• Enjoy dinner at a trendy restaurant in the area
• Experience Stockholm's nightlife at one of the many bars or clubs in the city

I hope this itinerary helps you plan your trip to Stockholm!