Numbers 7. Report of Colonel Lucius F. Hubbard, FIFTH Minnesota Infantry, SECOND Brigade, including operations May 2-22. WALNUT HILLS, near Vicksburg, MISS., May 25, 1863.

COLONEL: I have the honor to submit, for the information of your DEPARTMENT, the following details of the part sustained by the FIFTH Minnesota Infantry in the movements of the late campaign in this DEPARTMENT, which have culminated in the thorough investment of the rebel Gibraltar and its garrison at Vicksburg:

On the 2nd instant, the THIRD DIVISION of the Fifteenth Army Corps, of which the FIFTH Minnesota forms a part, left camp at Duckport, near Young's Point, La., and marched, via Richmond, to Hard Times Landing, crossing the river at the latter place to Grand Gulf, MISS., on the 7th instant. From thence we took the road toward Jackson, arriving at Raymond, 12 miles from the State capital, at about noon of the 13th instant. Here the FIFTH Minnesota was ordered to the front, with instructions to skirmish along the road and through the timber upon either flank, to feel for the enemy's outposts, and clear the way for the column to pass. We advanced about 4 miles before meeting obstructions, when a considerable body of rebel cavalry was encountered advantageously posted in a piece of woods in our front, from whence we received a sharp volley of musketry. I here deployed the entire regiment as skirmishers upon the right and left of the road, Lieutenant-Colonel Gere commanding the left wing. The enemy retired rapidly as we advanced, offering little resistance to our progress. I moved the line of skirmishers forward to Mississippi Springs, 1 1/2 miles, a point where several important pikes form a junction, and where I was ordered to halt, picket the roads, and bivouac for the night. The main column had halted and bivouacked where the enemy had been first encountered.

At daylight on the morning of the 14th, I was ordered to continue in the advance, and push forward on the Jackson road. A considerable body of the enemy had bivouacked the preceding night within one-half mile of my line of pickets, which retired as we moved forward. Owing to the broken and wooded nature of the country, and the known proximity of the enemy, we were required to move slowly and with extreme caution. For a distance of more than 5 miles I was required to keep in front of the column a strong line of skirmishers, consisting of three companies, which frequently encountered and exchanged volleys with the skirmishers of the enemy. When within perhaps 2 miles of Jackson, a determined stand was made, and a hot fire opened upon us from a full battery of artillery, supported by a strong line of infantry. At this juncture I was ordered by Major-General Sherman to deploy the balance of the regiment as skirmishers, covering the column while it should form in line, and penetrate forward as far as possible into a piece of timber in which the enemy was posted. As soon as the column as the column had deployed, the skirmishers were recalled, and the regiment took its position with the SECOND Brigade int the front line of battle. We then advanced and charged though the timber at double-quick, the enemy rapidly retiring within hi intrenchments near the precinct of the town. Here he made another stand, and obstinately disputed our farther progress. The fight continued for more than an hour, but was confined principally to artillery, the infantry occupying a position of shelter. At about 5 p. m. the order "forward" was given. All supposing