If you mean, "does the sequence [tex]a_n=\arctan(5n)[/tex] converge", then yes, since [tex]\lim\limits_{n\to\infty}\arctan n=\dfrac\pi2[/tex].
If you mean, "does the series [tex]\sum\limits_n\arctan(5n)[/tex] converge", then no, for the reason above (the summand passes the nth limit test for divergence, so the series diverges).
