To start: A very full and varied source collection includes most of the central sources for the Fifth Crusade.

Crusade and Christendom annotated documents in translation from Innocent III to the fall of Acre, 1187-1291 / edited by Jessalynn Bird, Edward Peters, and James M. Powell. Philadelphia : University of Pennsylvania Press, 2013.

Oliver of Paderborn

The Capture of Damietta

Oliver of Paderborn. Die Schriften des Kölner Domscholasters, Späteren Bischofs von Paderborn und Kardinal-Bischofs von S. Sabina Oliverus. Edited by Hermann Hoogeweg, Bibliothek des Litterarischen Vereins in Stuttgart 202. Tübingen: 1894.

English Translation: Crusade and Christendom, 158-225.

Jacques de Vitry

Letters

Jacques de Vitry. “Epistolae.” In Serta Mediaevalia: Textus varii saeculorum X-XIII, in Unum Collecti, edited by R.B.C. Huygens. CCCM 171. Turnhout: 2000.

Translation into French: Jacques de Vitry. Lettres de la Cinquième Croisade. Turnhout: Brepols, 1998.

Sermons

Jacques de Vitry’s Sermon to Pilgrims, 1229-1240.  Translated by J. Bird, in Crusade and Christendom, 141-153, from Douai BM ms. 503, fols. 370v-374r; Trecnto BC ms. 1670 (F55), fols. 100rb-102va.

Quinti Belli Sacri

Reinhold Röhricht. Quinti Belli Sacri Scriptores Minores. Geneva: J.-G. Fick, 1879.

Includes:
Philip of Oxford (?), “Ordinacio de predicationce S. Crucis in Anglia
Gesta crucigeorum Rhenanorum
De itinere Frisonium
Gesta obsidionis Damiate
John of Tudbia, De domino Iohanne, rege Ierusalem; Liber duellii christiani in obsidione Damieate exacti;
Fragmentum de captione Damiatae
Prophetiae cuiusdam arabica, in Latinorum castris ante Damiatam vulgate, versio quadruplex.

The Prester John Legend

Prester John. The Legend and its Sources. Compiled and Translated by Keagan Brewer. Ashgate, Farnham, 2015