What would happen if a cell is poked by a fine needle?
Generally speaking, there is no effect in microinjections.
This is relevant in the real world example of micro-injections. A video of a pronucleus injection can be seen here, or here is a more thoroughly explained procedure involving cloning. As you can see in the video the membrane, almost no effect will be observed - molecular dynamic simulations show that the membrane can spontaneously reform from fragments in the tens-of-nanoseconds timescale.
1/5 refers to  the question &quot;is the needle small enough?&quot;
The question does include the term &quot;1/5&quot;, which is a bit unusual. I guess they want you to recall a specific piece of information about the correct ratio size of needle should be. Here is a video of a microinjection at approximately that ratio. However the exit hole is unintentionally filled with the inserted material and cannot close immediately. The cell disappears out of frame before we can confirm the hole is closed.
Cell diameters are very variable
Cell sizes vary greatly.

From using these values, assuming a cell is a sphere an oocyte has a diameter of approximately 196µm, whereas a neutrophil has a diameter of 8µm. It's a bizarre question given this range because usually micro-needles are between 0.5 and 5 µm diameter in length, except in the case of oocytes where larger needles are used (according to wikipedia). I don't think this is relevant, and it is just arbitrarily picking a needle size that wouldn't completely maul the cell!