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If the homepage is in Google Directory, you can see a green bar next to the title (if the page is ordered on PageRank). This can help you to find out if you have a high PR5 or a low PR5. You can read more about it in The Handy Dandy Google PageRank Figurin' Guide V2.0 - See all 19 different possible PRs with examples [webmasterworld.com] and DMOZ and Google [webmasterworld.com].
Few of us would refer to that number as "exact", hence takagi's response.
There is a widespread belief in this community that the PR that the toolbar shows is derived from the real internal PR that the ranking algorithms use by a logarithmic transformation. The result is then rounded or truncated to an integer that is displayed on the toolbar.
There is a lot of speculation as to what base of logarithm is used, see a Google site search [google.com] for some discussions. Let us assume a base of 6, and truncation (rather than rounding) of the results.
If the toolbar shows you a PR of 5 it may represent an toolbar PR anywhere between 5.0 and 5.99999. The latter represents an internal PR six times as great as the former.
Hence the attempt to get a slightly closer approximation to the internal PR using the Google directory as takagi suggested.
<added>To answer your immediate question: Yes, get a newer version of the toolbar</added>