The Gospel this Sunday is St John 16:23-30. You can find the Matins readings for it over at my Lectio Divina blog.
This Sunday is the last in Eastertide proper - on Thursday the season changes to that sub-set of Easter, Ascensiontide. You can find notes on the rubrics for the Office during this period here.
In addition, the first three days of this week are traditionally especial days of prayer called Rogation Days, when the litany is sung in procession before the Mass.
The 1962 Benedictine Office this week in summary
Sunday 25 May – Fifth Sunday after Easter, Class II
Monday May 26 – St Augustine OSB, Class III/I [EF: St Philip Neri, Class III]; Rogation Day
Tuesday May 27 - St Bede the Venerable OSB, Class III/I; Rogation Day
Wednesday May 28 - Vigil of the Ascension, Class II; Rogation Day
Thursday May 29 - The Ascension of Our Lord, Class I
Friday May 30 – Class IV [EF: Commemoration of St Mary Magdalen of Pazzi]
Saturday May 31 – Saturday of Our Lady (Sat 5)