Get your taxes done using TurboTax

It is the IRS that limits it to $5,000, not TurboTax.

Per IRS instructions to Form 8888 Allocation of Refund (Including Savings Bond Purchases):

Use Form 8888 if:

• if you want us to directly deposit your refund (or part of it) to either two or three accounts at a bank or other financial institution (such as a mutual fund, brokerage firm, or credit union) in the United States, or
• You want to use at least part of your refund to buy up to $5,000 in paper or electronic series I savings bonds.

Each year, you can buy up to $10,000 in electronic Series I Savings Bonds or $20,000 per married couple.  

Here is where to go to purchase additional I Bonds:

Buying Series I Savings Bonds - Treasury Direct