I would think the NAS would be the better option. LTO5 can hold a lot but the media is a bit pricey and the speeds are not that spectacular compared to a good NAS, not to mention you need somebody on-site to rotate the tapes and such. A NAS would be quick and easy to automate and the date will be readily available at all time. Utilizing rsync with the NAS will speed up backups also.
Also, I haven't used LTO5 directly but in my experience at my day job, LTO4 tapes failed MUCH MUCH MUCH more frequently than the hard drives we were backing up to them. We eventually switched to "virtual tape" so now we backup to what's essentially a NAS after spending hundreds of thousands of dollars on our LTO/DLT backup system.
Depend on how accessible you need the data to be. Can be a tape for data security, it just sits in a box once it removed from the drive. With NAS you risk losing data on a hardware failure or the likes.
I would say your best bet is a good combo of both, regular backups to a NAS and backups to a hard copy as needed of more important data.
There have been plenty of times where we've gone to restore something only to find the tape is bad or the drive needs cleaning. Since moving to our virtual storage system we've only recently started seeing issues but we believe they are software related.
Also, tapes can be taken offsite easily. NAS hard disks aren't designed for that. AES256 hardware encryption is standard from LTO4 and above. There is definitely still a place for tape. I've only seen one bad tape in my lifetime (and many more bad HDDs), if you rotate your tapes properly they are very reliable.