Here's an ideal itinerary for 5 days in Taipei:

Day 1:

• Start your day with a visit to the iconic Taipei 101 skyscraper. Take the elevator up to the observation deck on the 89th floor for stunning views of the city.
• Afterward, head to the nearby Elephant Mountain for a hike and more breathtaking views of Taipei.
• In the afternoon, explore the Xinyi District, which is home to luxury shopping malls, trendy cafes, and restaurants.
• End your day by visiting the Raohe Street Night Market, where you can try some delicious Taiwanese street food.

Day 2:

• Begin your day by visiting the National Palace Museum, which houses one of the world's largest collections of Chinese art and artifacts.
• Afterward, take a stroll through the Beitou Hot Springs area, where you can relax in natural hot springs and enjoy the beautiful scenery.
• In the evening, head to the Shilin Night Market, one of the largest and most popular night markets in Taipei.

Day 3:

• Start your day by visiting the Chiang Kai-shek Memorial Hall, a national monument that honors the former President of the Republic of China.
• Afterward, take a walk through the historic Dadaocheng neighborhood, which is known for its traditional architecture and street food.
• In the evening, visit the Huashan 1914 Creative Park, a cultural center that hosts art exhibitions, live performances, and other events.

Day 4:

• Begin your day by taking a day trip to Jiufen, a charming mountain town that inspired the setting of the famous anime movie "Spirited Away."
• While in Jiufen, be sure to visit the old streets, tea houses, and temples.
• In the evening, return to Taipei and visit the Tonghua Night Market, which is known for its seafood and snacks.

Day 5:

• Start your day by visiting the Longshan Temple, one of the oldest and most famous temples in Taipei.
• Afterward, take a walk through the trendy Zhongxiao Dunhua neighborhood, which is known for its fashion boutiques and cafes.
• In the evening, visit the Ningxia Night Market, which is known for its traditional Taiwanese dishes and snacks.

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