Why does God allow suffering?

Why does God allow suffering? Why do we experience times in our life when we experience pain and tough times?
Does God care? Did He turn His back on us?
In Romans 5, Paul tells us that there is a purpose to our suffering. He writes we rejoice in our sufferings. How can that be possible? Who in the right mind says they rejoice in their suffering? It doesn't seem logically possible, to enjoy suffering. Yet the Bible tells us we need to rejoice in our sufferings. How can we?
In Romans 5, Paul tells us that there is a process that takes place when we suffer. Our suffering produces perseverance and patience. Trusting in the grace of God during tough circumstances results in our patience and perseverance. Through our perseverance, God is building our character. Our integrity and character is built through adversity. And our character is producing hope, which is found in Christ Jesus.
Points to ponder when going through tough times
1) God is desiring your whole heart, mind, soul
2) We are made for eternity (Our suffering is momentary compared to the glory of eternity)
3) When we go through suffering God is conforming us to the image of His Son
4) The suffering and trials we experience are only part of the journey, not the destination.
5) Rejoicing in our suffering doesn't mean we love the process, but we trust God that He has a plan in our lives