How much should I prepare for costs for 5 days to visit taipei only?

Hi, considering all, about 6000NTD is needed

6000nt?? No. That might just be the cost of a cheap-mid hotel.
Hotels usually run closer to 3000nt for something decent in Taipei (might some bargains for close to 2000, but anything less is going to be a dump).
Food wise, depends on you, but you can get buy on around 200-300nt (but only if you know where to get the local food - not mainstream restaurants).