How to find out Subversion repository version?

Have a look at <REPO>/db/format. After upgrading to 1.5 format, my format file shows:

3
layout sharded 1000

Before it used to be:

2

Take the http or https link to your repository and cut & paste it into a browser. The Subversion repository server version appears in the footer by default.

Powered by Subversion version 1.4.5 (r25188).

One would assume that a 1.4 server won't be running against a 1.5 repository.

For details, see the Subversion 1.5 Release Notes

Thanks to @Omus for the correction.

You can check the content of the file "format" under the "db" directory. If it shows 3 then it has been upgraded to 1.5 (that's the version of the updated fielsystem). If it is 2 then it is 1.4 or older.

There is a difference between Subversion Repository Version / Schema (1), and Subversion Repository FSFS Version (2).

FSFS, in contrast to Berkeley DB, or the developmental FSX, is a backend data storage method. FSFS is "a versioned filesystem implementation that uses the native OS filesystem directly".

(1): The Subversion repository version / schema is found in the [REPO]/format file. The current versions from the Subversion repos_upgrade_HOWTO document are:

SUBVERSION VERSION NUMBER           SCHEMA VERSION
-------------------------           --------------
Up to and including 0.27            1
0.28 - 0.33.1                       2
0.34 - 1.3                          3
(no released version used this)     4
1.4 -                               5

(2): The repository FSFS format however, is found in the [REPO]/db/format file. The current versions are in the libsvn_fs_fs FSFS Structure document, in the Filesystem formats section. They currently are:

Format 1, understood by Subversion 1.1+
Format 2, understood by Subversion 1.4+
Format 3, understood by Subversion 1.5+
Format 4, understood by Subversion 1.6+
Format 5, understood by Subversion 1.7-dev, never released
Format 6, understood by Subversion 1.8
Format 7, understood by Subversion 1.9
Format 8, understood by Subversion 1.10+

Also, as of Subversion 1.9 you can now use the svnadmin info command to gain both the Subversion Repository Version / Schema, as well as the Subversion Repository FSFS Version (See: Subversion 1.9 Release Notes - FSFS Improvements as well as Subversion 1.9 Release Notes - svnadmin Changes and Improvements)