Open problem about Pythagorean triangles

Definitions :

Square number
http://en.wikipedia.org/wiki/Square_number

Pythagorean Triangles and Triples

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html

Triangular number

http://en.wikipedia.org/wiki/Triangular_number

Pentagonal number

http://en.wikipedia.org/wiki/Pentagonal_number

Triangular numbers:
http://oeis.org/A000217

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431

Pentagonal numbers: n(3n-1)/2 :
http://oeis.org/A000326
0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151

The Open problem:

It asks for Pythagorean triangles with a triangular number and a square for legs, and a pentagonal number n(3n - 1)/2 for hypothenuse.

Are there any nontrivial examples besides (3,4,5) and (105,100,145)?
Does it help to allow pentagonal numbers of negative rank, n(3n + 1)/2?