The backup image contains only used extents, so it might be substantially smaller than the sum of tablespace sizes, depending on the tablespaces' types and their physical properties.
On the other hand, in DB2 10.5 the backup image will by default include log files that are modified during the backup, so depending on how active the database is during the backup you may need to include the log sizes into your calculation.
Finally, the backup image can be compressed. Compression ratio is impossible to estimate in advance.
As a result, you can only estimate the upper limit for free space required to store the backup image, which would be the sum total of the current tablespace sizes plus the size of included log files plus the backup image header.
See also this answer on Stackoverflow.