I have a computer with 5 hard drives, they are set up as Raid 5
the 5 hard drives are of same size (1TB each), and same brand (WD).
If I want to back up these 5 HDDs, do I have to use another 5 hard drive of same size and same brand? in another word, do I need to use another 5 hard drive from WD with 1TB each? or can I use 5 HDD with 1TB each but from different brand?
Question 2: after I backup these 5 HDD, I want to replace the original HDD with the backup HDD, and I expect it to work exactly the same as before. is it correct understanding?
The equation that determines the maximum space available in a RAID5 array that includes some number "n" of same-sized drives is (1 - 1/n) * n. In your case, this is (1 - 1/5) * 5 = 4/5 * 5 = 4, so the maximum space available on the array is 4 * 1TB = 4TB.
To back this up, you do not actually need another RAID5 array; you could simply back it up to a single 4TB drive.
If, on the other hand, the goal is to create a replacement RAID5 array that holds the same data, then you need an array that contains some number of drives that offers a maximum space of 4TB or more. For example, a RAID5 array containing three 2TB drives will also have a maximum space of 4TB (Is this a test? Do I need to show my math?).
As for using drives from different manufacturers, this is usually not an issue. You do need to account for their size representation, however. If one manufacturer uses true megabyte representation (i.e. 1MB = 1048576 bytes) and another uses million-byte representation (i.e. 1MB = 1000000 bytes), then you cannot copy the former, if full, to the latter; there simply isn't enough room. The good news is that most hard drive manufacturers consistently use the latter as it makes their drives look bigger then they actually are 😉.
Hope this helps,