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congruent n.  and  pentagonal n.

First numbers that belong to both sets:

5, 22, 70, 92, 117, 145, 210, 247, 287, 330, 376, 477, 532, 590, 651, 782, 852, 925, 1080, 1247, 1335, 1520, 1717, 1820, 1926, 2035, 2262, 2501, 3015, 3151, 3290, 3725, 4030, 4510, 4676, 4845, 5551, 5735, 5922, 6112, 6305, 6501, 6902, 7526, 7740, 7957, 8400, 8855, 9087, 9560, 10045, 10292, 10542, 11310, 11572, 11837, 12376, 12927, 13207, 13776, 14357, 14652, 14950, 15862, 16485, 17120, 17767, 18095, 19437, 20126, 21182, 21901, 22265, 23375, 23751, 24512, 25285, 26070, 27270, 27676, 28085, 28912, 29751, 30175, 31032, 31901, 32340, 32782, 34126, 34580, 35037, 35960, 36895, 37367, 38801, 39285, 39772, 40262, 41750, 42757, 44807, 45327, 47437, 48510, 50142, 50692, 51245, 53487, 54055, 55200, 56357, 57526, 59302, 59900, 60501, 61105, 62935, 63551, 64792, 66045, 66676, 67310, 69230, 69876, 70525, 71832, 73151, 73815, 76501, 77180, 77862, 79926, 80620, 81317, 83426, 84135, 84847, 87725, 89182, 91390, 92877, 95887, 96647, 98176, 99717, 101270, 103622, 104412, 105205, 108407, 109215, 110840, 112477, 113300, 114126, 116622, 117460, 118301, 119992, 121695, 122551, 124272, 126005, 126876, 127750, 130390, 131276, 132165, 133952, 134850, 135751, 136655, 140301, 142142, 143995, 144926, 146797, 150575, 151527, 153440, 154401, 155365, 156332, 157302, 160230, 161212, 162197, 164176, 166167, 167167, 168170, 169176, 170185, 171197, 172212, 173230, 176302, 177332, 178365, 180440, 182527, 183575, 184626, 185680, 186737, 187797, 188860, 189926, 190995, 193142, 195301, 197472, 199655, 200751, 205165, 206276, 207390, 210750, 211876, 213005, 217551, 218695, 220992, 223301, 225622, 229126, 230300, 231477, 233840, 236215, 237407, 238602, 239800, 241001, 242205, 243412, 244622, 247051, 248270, 249492, 250717, 253176, 255647, 256887, 258130, 261877, 263132, 264390, 268182, 270725, 273280, 275847, 277135, 278426, 282317, 284926, 288862, 291501, 292825, 296815, 298151, 303525, 306230, 307587, 310310, 311676, 313045, 318551, 319935, 322712, 324105, 325501, 326900, 328302, 332526, 333940, 335357, 338200, 341055, 342487.

Some larger examples :