DSolve[{Sin[x2[t]]*Derivative[1][x1][t] == Sin[x3[t]]*x4[t] + Cos[x3[t]]*x5[t], Derivative[1][x2][t] == Cos[x3[t]]*x4[t] - Sin[x3[t]]*x5[t], Cos[x2[t]]*Derivative[1][x1][t] + Derivative[1][x3][t] == a, -(a*(1 - lambda)*x5[t]) + Derivative[1][x4][t] == -(m*Cos[x3[t]]*Sin[x2[t]]), a*(1 - lambda)*x4[t] + Derivative[1][x5][t] == m*Sin[x2[t]]*Sin[x3[t]]},{x1[t], x2[t], x3[t], x4[t], x5[t]},t]