Q.If the effective (rms) current in a 50 cycle AC circuit is 5 A, what is the peak value of the current? What is the current 1/600 s after it was zero?

Because an alternating current or voltage constantly changes both its magnitude and its sign throughout each cycle, a single steady number is needed to usefully describe its 'typical' size -- and two different such numbers are standard, each answering a different practical question. The AVERAGE value, $i_{av}=0.637\,i_0$ (equivalently $e_{av}=0.637\,e_0$), is defined over only a HALF cycle, since the average taken over a FULL cycle is always exactly zero (the positive and negative halves of the sinusoid cancel perfectly) and so is not a useful descriptor at all.

The RMS (root-mean-square, also called effective or virtual) value is defined differently, via the heating effect of the current: $i_{rms}$ is the value of a steady DC current that would produce exactly the same amount of heat, in the same resistance, over the same time, as the actual alternating current does. Since heat production depends on $i^2$ (always positive, regardless of the current's instantaneous direction), this quantity never averages to zero, making it a genuinely useful representative value. Working through the averaging gives $i_{rms}=i_0/\sqrt2\approx0.707\,i_0$ and, identically, $e_{rms}=e_0/\sqrt2$. Ordinary AC ammeters and voltmeters are built to display this rms value -- which is exactly why a '220 V AC' supply is understood to mean an rms value of 220 V, even though the instantaneous voltage actually swings all the way up to a peak of $\sqrt2\times220\approx311$ V within every cycle. A moving-coil meter, by contrast, responds to the (always-zero) average value and so cannot be used to measure AC directly at all.