Can somebody please help me with this question?

Explanation:

I believe the answer would be:

Te2- > I- > Cs+ > Ba2+ > La3+ (from biggest to smallest)

This is what you wrote above.  This makes sense because all 5 ions are isoelectronic with xenon (i.e. they all have 54 electrons) but the number of protons (positively charged particles in the nucleus of the atom) of each is different:

La3+ has 54 electrons and 57 protons, meaning that there are 3 additional positive charges to attract the negatively-charged electrons, bringing them closer in towards the nucleus (a "stronger" grip, and therefore, smaller-sized ion if you can imagine).  

Ba2+ has 54 electrons but 56 electrons (only 2 additional positive charges).  

Cs+ has 54 electrons and only 55 protons (only 1 additional positive charge).

I- has 54 electrons and only 53 protons (1 fewer positive charge).

Te2- has 54 electrons and only 52 protons (2 fewer positive charges).

Anions (negatively charged ions) that are isoelectronic with a particular noble gas (in this case, xenon) are generally larger in size than cations (positively charged ions) that are also isoelectronic with the same noble gas.

since the atomic number is the number of protons in the nucleus, as we move to the left on the periodic table, the electrostatic pull between the nucleus and the valence electron shell decreases. as we move down a group (vertical column), the valence shell energy level gets further and further from the nucleus.