I have a data set of 619 adult and 619 adolescent respondents indicating their behaviour in a five point scale. Which statistical test can be used to test if there is any difference in the behaviour of adults and adolescents?
I assume that when you say "five point scale" that you have a single 5-point Likert item.
In this is the case,
The Cochran-Armitage test is an ideal test.
Ordinal regression is also ideal, though more difficult in some software.
The Mann-Whitney test is commonly used in this case, although there is some controversy about using it for an ordinal dependent variable with few ties.
In any case, I would recommend reporting an effect size statistic. A significant p-value by itself may not tell you very much.
r ---- the one appropriate for Mann-Whitney ---- is the most common
epsilon-squared, Freeman's theta, and Kendall's tau-b are also options.
Some information on interpreting these statistics is here: http://rcompanion.org/handbook/F_04.html
Also consider expressing the results graphically. Histograms of counts for each group would be very effective.
It depends how your variable is distributed. If highly skewed or non-normal, then it would be better to use a non-parametric test, most likely Mann-Whitney since you only have two comparison groups. If your variable is relatively normal, then you can simply use a standard t-test.