I really appreciate your keenness on performing the five daily prayers on time and keeping your duty towards your Creator. Almighty Allah always tells us that we should try to fulfill our duties to the best of our abilities and that He will not place us in hardships or cause us any type of suffering.
Working to feed oneself and one's family is itself a form of worshipping Allah by being good, and productive. Yet, as organized people, we should bear in mind that for every hour there is a specific act of worship and the smart and balanced one is the one who keeps on doing the worship in its due time and never be busy with something else.
Before I go ahead tackling the core of your question, I would like to highlight that this answer is not a fatwa and cannot be so. If you need a fatwa, I will advise you to seek the fatwa of your local Imam after explaining the whole situation to him because I believe he will be the most efficient one to give the most suitable Shari`ah-compliant solution.
I cannot give you a fatwa that you are allowed to do the five prayers at one go, because this is not feasible and this is not the place to issue fatwas.
What you will be reading here is some pieces of advice all aiming at facilitating the situation for you and trying to sort out some venues through which your life can become easier while you are still observing your duties towards Almighty Allah.
The first step towards an effective solution is to realize the fact that Islam can be incorporated into our life styles; it is not alien to it. We can lead a life of pleasure and happiness while it is an Islamic life at the same time.
The problem which happens in the minds of many of us is when we think that following the teachings of Islam will prevent us from feeling the sweetness of life.
I assure you, you can keep your duty towards Allah and at the same time get the enjoyment of life. It only takes some tactics and plans to sort out some easy ways on how to fit these teachings in our life. And once they are integrated in the system, we will realize that they are indispensible and they do add meaning to our existence.
How can we do this though? How can we carry the theory to the practical field?
The first step, is to realize the importance of prayers and their value and what position should be given to them according to this importance.
For instance, when someone comes home from work and he is so tired and in bad need to sleep, does he forget to spare five minutes to eat before he goes to bed? Suppose that the food is not ready and he preferred to go and have a nap until it is ready, does not he wake up for minutes to eat and then go back to sleep. Suppose in the middle of one's sleeping, he felt the need to go to the toilet, does not he wake up to go to the toilet?
Obviously the answer to all the previous questions will be yes, he will interrupt his sleep and wake up to do any of the aforementioned things. Why? Because such things are very important and indispensible in man's life, he cannot do without them.
Therefore, we need to realize the importance of prayer to us, being the thing that connects us to our Creator, the way through which we seek His Blessings and Bounties.
Can you spend your life without food, drink or going to the toilet? The answer will simply be 'No' and we should ask then another question, 'Can you spend your life without prayer?' You will say 'No'.
Now, a second question, 'Can you delay going to the toilet when you need to go?' The answer again is no and I will pose the same question regarding prayer and leave the answer to you.
I think for a couple of prayers which you miss during the day, you can simply set the alarm at the time of each and wake up to do it in five minutes and resume your sleeping. I know this is going be tough at the beginning, but by the lapse of time you will be accustomed to it, and again, it will become a part of the system of your life.
We do learn things by habituating ourselves to them i.e. by making them habits in our life through doing them so frequently. You can simply do this and I believe it deserves an attempt, doesn't it?
You do not have to leave your work or change the system of your life, all you have to do is to adapt the system of your life to be more productive and more God-oriented.
The second step, increase the love of prayer in your heart because when someone is in love with something, he will awaken all his body to it. What about if after a long night of work you are told to go home, rest for an hour and wake up again?
The need of work will make you set an alarm and you may even wake up on time without a need for an alarm. If you are waiting for a relative or someone dear to you, you do not have to have a reminder even to remind you of the time because it is already engraved in your heart.
I think if we adopt this mentality, we will end up adapting our day around the prayer times, we will find no difficulty in doing our work and at the same time fulfilling our duty towards Allah. One of the scholars used to sleep for 3 hours only everyday and he used to work in dawah all the day. When he was asked how he could manage sleeping only for three hours, he asked people in return: 'Why do we need sleep?' They said: 'To rest.' He commented: 'what about if dawah work is your rest and happiness, will there be any need of sleep at all?'
Finally, pray to Allah to help you fulfill what He has required from you for definitely He is near to answer your supplication.