Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(5 x + 4 \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = - \frac{4}{5}$$
$$x_{2} = - \frac{4}{5} + \frac{\pi}{5}$$
Numerical solution$$x_{1} = 36.2707933123596$$
$$x_{2} = 90.306186954104$$
$$x_{3} = 9.8814150222053$$
$$x_{4} = 80.2530904626167$$
$$x_{5} = 63.9168086639497$$
$$x_{6} = 28.1026524130261$$
$$x_{7} = 100.359283445591$$
$$x_{8} = -61.746897479642$$
$$x_{9} = -27.8176968208722$$
$$x_{10} = -83.7380460547705$$
$$x_{11} = 92.1911425462579$$
$$x_{12} = -68.0300827868216$$
$$x_{13} = -46.038934211693$$
$$x_{14} = 34.3858377202057$$
$$x_{15} = 78.3681348704628$$
$$x_{16} = 53.8637121724624$$
$$x_{17} = -78.0831792783089$$
$$x_{18} = -2.05663706143592$$
$$x_{19} = -69.9150383789755$$
$$x_{20} = 7.99645943005142$$
$$x_{21} = 58.2619418874881$$
$$x_{22} = 14.279644737231$$
$$x_{23} = -0.8$$
$$x_{24} = -19.6495559215388$$
$$x_{25} = -91.906186954104$$
$$x_{26} = -25.9327412287183$$
$$x_{27} = 2.34159265358979$$
$$x_{28} = 62.0318530717959$$
$$x_{29} = 31.8725635973339$$
$$x_{30} = 70.1999939711293$$
$$x_{31} = -17.7646003293849$$
$$x_{32} = 19.9345115136926$$
$$x_{33} = -35.9858377202057$$
$$x_{34} = -12.1097335529233$$
$$x_{35} = 89.0495498926681$$
$$x_{36} = 38.1557489045134$$
$$x_{37} = 4.22654824574367$$
$$x_{38} = -73.6849495632832$$
$$x_{39} = -13.9946891450771$$
$$x_{40} = 739.359229185755$$
$$x_{41} = 60.146897479642$$
$$x_{42} = -7.71150383789755$$
$$x_{43} = 72.0849495632832$$
$$x_{44} = 56.3769862953342$$
$$x_{45} = -95.6760981384118$$
$$x_{46} = 96.5893722612836$$
$$x_{47} = -37.8707933123596$$
$$x_{48} = 16.1646003293849$$
$$x_{49} = 94.0760981384118$$
$$x_{50} = 111.040698467797$$
$$x_{51} = -81.8530904626167$$
$$x_{52} = -100.074327853437$$
$$x_{53} = -90.0212313619501$$
$$x_{54} = 18.0495559215388$$
$$x_{55} = -59.8619418874881$$
$$x_{56} = -15.879644737231$$
$$x_{57} = -63.6318530717959$$
$$x_{58} = 14836.3137843739$$
$$x_{59} = -34.1008821280518$$
$$x_{60} = 17.4212373908208$$
$$x_{61} = -47.9238898038469$$
$$x_{62} = -35.3575191894877$$
$$x_{63} = -56.0920307031804$$
$$x_{64} = 82.1380460547705$$
$$x_{65} = -49.8088453960008$$
$$x_{66} = -57.9769862953342$$
$$x_{67} = 40.0407044966673$$
$$x_{68} = -29.7026524130261$$
$$x_{69} = 112.925654059951$$
$$x_{70} = -52.9504380495906$$
$$x_{71} = 24.3327412287183$$
$$x_{72} = 26.2176968208722$$
$$x_{73} = -45.4106156809751$$
$$x_{74} = -39.7557489045134$$
$$x_{75} = 46.3238898038469$$
$$x_{76} = 85.9079572390783$$
$$x_{77} = -41.6407044966673$$
$$x_{78} = 6.11150383789755$$
$$x_{79} = 51.9787565803085$$
$$x_{80} = 29.98760800518$$
$$x_{81} = -51.6938009881546$$
$$x_{82} = -8.3398223686155$$
$$x_{83} = -3.94159265358979$$
$$x_{84} = 73.9699051554371$$
$$x_{85} = -88.1362757697963$$
$$x_{86} = -5.82654824574367$$
$$x_{87} = 95.9610537305656$$
$$x_{88} = 50.0938009881546$$
$$x_{89} = -24.0477856365645$$
$$x_{90} = 68.3150383789754$$
$$x_{91} = -93.7911425462579$$
$$x_{92} = 48.2088453960008$$
$$x_{93} = 84.0230016469244$$
$$x_{94} = -71.7999939711293$$
$$x_{95} = -85.6230016469244$$
$$x_{96} = 41.9256600888212$$
$$x_{97} = -79.9681348704628$$