First of all make a rough sketch. Do not start construction without drawing a rough sketch showing sides, angles and diagonals, etc., with correct name.
Step I. Draw a rough sketch and mark the measurements.
Step II. Draw AC = 7 cm.
Step III. With A as centre and radius 4 cm, draw an arc above AC.
Step IV. With C as centre and radius 6 cm, draw another arc intersecting the previous arc at B.
Step V. With centre A and radius 5.5 cm, draw an arc below AC.
Step VI. With centre C and radius 5 cm, draw another arc to intersect the previous arc at D.
Step VII. Join DA and DC.


Thus, ABCD is the required quadrilateral.

Solution not provided.

No, any 5 measurements (elements) cannot determine a quadrilateral. Actually to construct a quadrilateral, we need a specific combination of measurements such as:

(a) Four sides and one diagonal.
or
(b) Three sides and two diagonals.
or
(c) Two adjacent sides and three angles.
or
(d) Three sides and two included angles.
or
(e) Some special properties are given.

Let us draw a rough sketch of BATS as given.
Here, we cannot locate the points T and B without knowing the measurements ST and SB respectively.
Thus, we cannot draw a parallelogram with the given measurements.