Sorry for the length, this turned into a lengthier explanation than I imagined. I've been looking at backup solutions for 32TB for a colleague...
When you say 5TB, is that the size for a full backup? How frequently will you be doing full/increment/differential, and how much data to do anticipate for them. How much time can you afford for the backup to run for?
Just for the full backup, for example (very quickly searched, based on first results, some are internal tape units):
An LTO-3 tape drive will cost about $200, a tape will hold 0.4T @ $20, so you'd need 13 tapes, totaling $260. It runs at 80MB/s, which takes roughly 18hrs to run, including a little time to switch tapes.
An LTO-4 tape drive will cost about $600, a tape will hold 0.8T @ $16, so you'd need 7 tapes, totaling $112. It runs at 120MB/s, which takes roughly 12hrs to run, including a little time to switch tapes.
An LTO-5 tape drive will cost about $1400, a tape will hold 1.5T @ $22, so you'd need 4 tapes, totaling $88. It runs at 140MB/s, which takes roughly 10hrs to run, including a little time to switch tapes.
An LTO-6 tape drive will cost about $1800, a tape will hold 2.5T @ $30, so you'd need 2 tapes, totaling $60. It runs at 160MB/s, which takes roughly 9hrs to run, including a little time to switch tapes.
An LTO-7 tape drive will cost about $3500, a tape will hold 6T @ $35, so you'd need 1 tape, totaling $35. It runs at 140MB/s, which takes roughly 5hrs to run, including a little time to switch tapes.
Now account for your in-between full backups, that all depends on how much change you experience. For example, 10% change per day would in the LTO3 case be about 1 tape per day, so assuming a full once per month, that's roughly 30 more tapes.
Now we get into retention:
If you want 3 months (again LTO3), we're at a total of (13+30)*3=129 tapes ($2580 in media cost). Now that $3500 LTO7 tape drive doesn't seem so bad considering you need 9 tapes in total, for $315. So you can see how it begins to even out.
Also in the LTO3 case, for example, an overnight full backup requires a human to change tapes every 80 minutes, so there's another cost to consider. Alternatively you can get a robot tape changer, but that's going to jack you up into some serious money.
By comparison, a cloud backup, running at say 5MB/s (50mb/s), would take 12 days to run.
A RAID in another building over a gigabit connection is another option, but backup to disk is risky because a serious power event can take out everything. Before I started working here, during a storm a tree fell, causing a 60kv line to fall onto a 6kv line (I think) and fried just about every electronic device on the property. Blew up UPS's as well.
Other considerations are how frequently are you going to test the media, how long can you afford when a restore is needed and finally the cost of backup software.
So it's a question of time, budget, fluidity of change, retention period, how many tapes you want to juggle, cost of administering; versus the risk.
