No, regardless of your goals, that is not a good workout routine.
a) No leg work, b) no back work, c) too much pushing work, d) too much arm work.
Assuming from your question that you can train on Monday / Tuesday / Thursday / Friday, then you'd be much better doing either a push / pull split, or an upper lower split.
How this would look is either:
- Monday - Light / moderate pull
- Tuesday - Light / moderate push
- Thursday - Heavy pull
- Friday - Heavy push
(for a routine, something like this, but with the days swapped slightly so you get more rest after the heavy pull / heavy push days)
- Monday - Upper
- Tuesday - Lower
- Thursday - Upper
- Friday - Lower
(I'm not going to give you a specific one, just have a search around, there's too many to count)
If you go with your current routine, you're going to be limiting your muscle growth potential by not doing some of the major compound exercises, you're going to give yourself shoulder issues because of the lack of pulling exercises to offset the pushing and even if neither of those come to pass, you're going to end up looking like Johnny Bravo (and very probably be laughed at for your lack of legs).