Question

an element in period 2 has the following successive ionization energies. Identify the element. IE1=801kJ/mol IE2=2427 kJ/mol IE3=3659kJ/mol IE4=25,022kJ/mol IE5=32,822

Answer 1

I will assume that the 25,022kJ the highest one IE4 is the one to remove one electron from the element with the electron configuration of the Noble gas, in this case since the element is in the second period will be He. Then you will have the Li IE3, Be IE2 and the B with the IE1.
I would double check in some reference table for correlation
http://www.webelements.com/boron/atoms.html

Ionisation Energies and electron affinity
The electron affinity of boron is 26.7 kJ mol‑1. The ionisation energies of boron are given below.

Ionisation energies of boron
Ionisation energy number Enthalpy / kJ mol‑1
1st 800.6
2nd 2427.1
3rd 3659.7
4th 25025.8
5th 32826.7

Answer 2

Thank you Cuanchi