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I assume your approach would be one full and the rest incremental backups.<br />
For this purpose you can get one of Symantec, Acronis, Shadow Protect, Parafon backup tools and let them backup your data.<br />
As hardware backup solution Barracuda backup or simmilar would suit for your needs.
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I tried Symantec but external USB hard drive not good if more than 2TB!<br />
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I have few external hard disk(USB 3) which I can connect as required (Daily, weekly, monthly) once it's labelled/configured on backup software!<br />
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Barracuda backup hardware is like external USB or like tape drive?
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Why to external USB and not to an offsite or cloud service?
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I &nbsp;believe Intronis (web-based backup system) will allow you to take an initial snapshot manually to disk, then replicate the daily/whatever-interval backups directly over the web.
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The fastest way to backup that amount of data would be using a bit-level backup like Storagecraft ShadowProtect. &nbsp;It will still be a bit slow, I think, writing to a USB drive, but it would be a lot faster than a file level backup like Backup Exec. &nbsp;Storagecraft is designed to backup directly to an internal hard drive and then can be configured to mirror that backup to external USB or other type of storage. &nbsp;It can, however, be configured to write directly to an external drive if required.
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We like the Datto solutions and offer solutions based on Asigra and eVault. &nbsp; Keep in mind that USB is slow. &nbsp;Recovery tops out at ~3GB per minute. &nbsp;<br />
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We have solutions that can restore at ~30-35GB per minute and/or provide a virtual recovery environment that can have you up and running within minutes.
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Thank you guys.. right now I am trying Syncback Pro which looks promising :)<br />
I will also try Strogecraft and will see...<br />
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@Allen wish to know more about the solution you have mentioned 30GB/min!
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Instant recovery is built into the Datto Siris appliances and service. &nbsp;<br />
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We partner to provide RestartIT. &nbsp;It's offsite backup but instead of shipping USB drives for large recovery, we ship a full mobile vault. &nbsp;A server with your encrypted data. &nbsp;You plug it into your betwork and restore at speed based on SATA arrays and gigabit Ethernet instead of USB 3.
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As the asker ignored this question for a while I assume he found a solution for his needs.
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5TB Data needs to backup daily weekly monthly to external USB on Windows server 2008 R2- <br />
<br />
What's the quickest and Best way ? PAID software or hardware also fine if that is consider as BEST,EASY and realiable!
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5TB Data needs to backup daily weekly monthly to external USB on Windows server 2008 R2- 

What's the quickest and Best way ? PAID software or hardware also fine if that is consider as BEST,EASY and realiable!

5TB Data needs to take regular backup from Windows server 2008 R2 file server to external USB

Windows Server 2008 and Windows Server 2008 R2, based on the Microsoft Vista codebase, is the last 32-bit server operating system released by Microsoft. It has a number of versions, including including Foundation, Standard, Enterprise, Datacenter, Web, HPC Server, Itanium and Storage; new features included server core installation and Hyper-V.

Windows Server 2008

The term "Backup" means the methods and processes involved to copy computer data (system data as well as application data) to media other than the ones where the data originally live (disk, tape, optical, cloud). "Restore" in turn means the methods and processes involved in data recovery, i. e., bringing back copied computer data to their original location. Backup/Restore primarily serves as a means of protection against data loss, be it due to disaster, corruption or sabotage. It can also be used for recovering data from an earlier point in time and even for cloning machines or applications. There is a wide variety of backup/restore software available, from expensive commercial products to free or open source tools.

Storage Software

Storage devices include any device used for storing and retrieving digital information. Hard disk drives (HDDs) use one or more rigid ("hard") rapidly rotating disks (platters) coated with magnetic material. Data is accessed in a random-access manner, meaning that individual blocks of data can be stored or retrieved in any order and not only sequentially. The primary competing technology for secondary storage is flash memory in the form of solid-state drives (SSDs), but HDDs remain the dominant medium for secondary storage due to advantages in price per bit and per-device recording capacity. CD-RW (Compact Disc-ReWritable) is a digital optical disc storage format that allows information to be stored outside the mechanical HDD.

Storage Hardware

Cloud computing, also known as on-demand computing, is a kind of Internet-based computing where shared resources and information are provided to computers and other devices. It is a model for enabling ubiquitous, on-demand access to a shared pool of configurable computing resources. Cloud computing and storage solutions provide users and enterprises with various capabilities to store and process their data in third-party data centers, relying on sharing of resources to achieve coherence and economies of scale.

Cloud Computing

Acronis sets the standard for cyber protection and hybrid cloud storage through its innovative backup, anti-ransomware, disaster recovery, storage, and enterprise file sync and share solutions. Powered by the Acronis AnyData Engine and strengthened by innovative artificial intelligence and blockchain technologies, Acronis solutions deliver easy, reliable, efficient, secure, and private cyber protection.  Founded in Singapore in 2003, Acronis is celebrating its 15-year anniversary. Supported by more than 1,000 employees worldwide, Acronis’ products are used in over 150 countries, delivering complete protection to more than 5 million consumers and 500,000 businesses. Learn more at acronis.com