Firing/laying off non-political appointee federal employees, aka civil service employees, will do nearly nothing to save money. The Federal government isn't a software company where one of the most expensive things is the cost of people.
If the budget is about $6,000B per year, 5% of that is $300B and if the target is laying off 10%, you are talking $30B. It sounds like a lot of money to a person but that means your federal budget is now $5,970B.
Basic budgeting concepts - if you wanted to save a lot of money you wouldn't be looking at something which only accounts for 5% of your budget. It would be like if your personal debt keeps increasing each year and you have a $800/mo car payment, $4000/mo mortgage, etc. and think eliminating 1 coffee run per week will save you.