we have a huge database that has almost five years of data.

Is it possible to perform Database backup for each year ? or is it only complete full backup can be performed?

No, it is not possible to generate a full backup up of just "portions" of a database - generally speaking. 

we have a huge database that has almost five years of data.

Is it possible to perform Database backup for each year ? or is it only complete full backup can be performed?

If you have Enterprise edition, you can partition the table into multiple filegroups (1 per year of data) and do a file group backup. Going this route would allow you to roll off old data as it becomes too old and loses its value.

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• Proposed as answer by Lydia ZhangMicrosoft contingent staff, Moderator 3 hours 47 minutes ago

can i check if the table is already partitioned into filegroups and if not then perform partition.

Also I dont think the partitioning of the table requires any downtime.

Here a script that shows all partitionned tables:

Select s.name As SchemaName, t.name As TableName
From sys.tables t
Inner Join sys.schemas s On t.schema_id = s.schema_id
Inner Join sys.partitions p on p.object_id = t.object_id
Where p.index_id In (0, 1)
Group By s.name, t.name
Having Count(*) > 1
Order By s.name, t.name;

The partitionning does not require downtime.

Also I dont think the partitioning of the table requires any downtime.

It do; you are going to move data from the main to an other partition and this will cause locks on the table.