The membership analysis of Rees (1993) includes 515 stars in the magnitude
interval 10.9 < V < 15.7 covering the central 12 
12 arcmin
region of M 5. Only 33 per cent of these stars are located outside of
5 arcmin from the cluster centre. Allowing half an arcsec differences
in the coordinates we matched 149 stars from the catalogue of Rees (1993)
with our sample.
Figure 5: Comparison of different membership probabilities with the
accurate membership probabilities of Rees (1993): a) 
,
b) 
,
c) 
. The last plot d) shows the histogram of
averaged membership probabilities 
(not the average of the histograms b) and c)). The solid line
shows the histogram of our membership probabilities for cluster members from
Rees (1993) whereas the dashed line shows the
histogram of our membership probabilities for non-members from
Rees (1993). From 149 cross-identifications
with the catalogue of Rees (1993) only the
objects with total proper motion errors of less than 7 mas/yr are
included in the comparison. As far as only a region close to the
cluster centre could be used for the comparison, our membership
probabilities based only on the proper motions (affected by larger
errors due to crowding effects near the cluster centre) show the
worst result
The relative proper motions of Rees (1993) are extremely accurate:
with total proper motion errors ranging from 0.15
mas/yr in the inner cluster region (r < 8 arcmin) to about 0.30
mas/yr for the stars in the outer cluster region of his catalogue (
12 arcmin). He achieved a further improvement in comparison to the former
work of Cudworth (1979) by including more plates and by a
modified proper motion and membership derivation. The proper motion accuracy
of our catalogue is more than 10 times worse (cf. Fig. 1 (click here)) with a
different trend (better accuracy in outer cluster region compared to the
inner region) caused by image crowding. Due to the much better proper motion
accuracies of Rees (1993) we can use his membership
probabilities as 100% true reference.
In order to compare our membership probabilities with those of Rees (1993)
we did not exclude the inner cluster region (r < 5 arcmin) but instead
decided not to use the stars with large total proper motion errors.
From 104 stars with total proper motion errors of less than 7 mas/yr
there were 82 members and 22 non-members according to Rees (1993).
Figure 5 (click here) shows the histogram of our membership probabilities for these
true members (solid lines) and non-members (dashed lines).
In addition to the membership probabilities 
and 
we plotted the histogram of the averaged membership probabilities
.
If we define from our membership analysis all stars above a certain
membership probability level as members and all stars below that level
as non-members, so we obtain in the best case (at the level 
) 85
per cent of all 104 stars having the same membership classification as
given by Rees (1993). The next best segregation is obtained with
(correct membership classification for 82.5
per cent of the stars). As far as only a region close to the cluster centre
could be used for an external comparison of our membership probabilities
the reliability of our membership probabilities in the outer cluster region
can only be estimated on the basis of the knowledge of the mean proper
motion and number density of the field stars using relationship (7) and
by comparison with the CMD of the cluster (see previous section).
Figure 6: Projected surface density profile of M 5.
Logarithm of surface density in stars per arcmin
versus
logarithm of the mean annulus radius 
[arcmin].
The line shows the best fit with the empirical
density law from King (1962). In the fitting procedure
only the star counts (dots with error bars) and the data
from King (1966) (crosses) were used. Also shown are the
data from Kron et al. (1984) (triangles) and from
Kron & Mayall (1960) (boxes). The dotted line indicates
the background surface density