No zeros, yet still affecting stability?
As you've more or less drawn it, the overall transfer function is (assuming here that \$G(s)\$ is actually the transfer function of the plant, the transfer function enclosed by the box in your drawing)

$$H(s) = \frac{G(s)}{1 + G(s)}=\frac{K\cdot 50}{s^4 + 15s^3+ 100s^2+250^s + K\cdot 50}$$

So it's easy to see that the gain \$K\$ will affect the location of the poles.

Indeed, putting this into Wolfram Alpha with \$K = 100\$ shows two poles in the RHP.

You should try doing a root locus analysis to see how those poles move from the LHP to the RHP as \$K\$ is increased.