You don't enter or use the 5498.  After you enter each 1099R you keep going and it will ask what you did with it.  You can say you moved it to another account.  What codes are in box 7?  If it is a G that is for a Direct Rollover and that's all you enter.

 If you are looking at a summary screen or review screen those show the full amount as income and lump a lot of stuff together. You need to check the actual 1040 and make sure it’s right.   For 1099R check 1040 line 4b for any taxable amount.  If it was a rollover it should say ROLLOVER by it. 

These were not direct rollovers, but :

1. a check issued by institution 1 and check deposited into institution 2 (within 60 day window).

2. Multiple cash withdrawls made, and single deposit made within 60 days. 

The financial institution recorded these on 5498, and since all withdrawals were via check they issued 1099 as normal distributions. 

My question is HOW TO ENTER THIS INFO INTO TURBO TAX??

As I said you just enter each 1099R and answer the follow up questions.  It will ask what you did with it.  Do they have code 7 in box 7?  What kind of account did you roll it over from?  401K or other IRA?  What did you move it to?  If it was to a ROTH IRA it may all be taxable. @dmertz  

Enter a 1099R under

Federal Taxes on the left side

Wages & Income at the top

Then scroll way down to Retirement Plans and Social Security,

Then IRA, 401(k), Pension Plans (1099R) - click Start or Revisit

If you are filing a Joint return be sure to pick which person it is for.

1.  Indirect rollovers are entered into TurboTax by entering the Form 1099-R that reports the distribution from the original retirement account and in the follow-up indicating that the money was moved to another retirement account (or returned to the same account), then indicating how much of the distribution was rolled over.  The gross amounts of all Forms 1099-R will be included on 2019 Form 1040 line 4a but amounts reported as rolled over will be excluded from the taxable amount on line 4b.  Only the amount on line 4b adds to your taxable income.

2. If the multiple cash withdrawals were from IRA accounts rather than from a qualified retirement plan, it appears that you have violated the statute that limits you to one IRA-to-IRA rollover in any 12-month period.  Deposits after the first one, those that that violate this rollover limitation, are excess contributions subject to penalty. The limitation is on the number of distribution eligible for rollover, not on the number of rollover contributions (deposits).  Distributions from an IRA are indicated by either having the IRA/SEP/SIMPLE box marked (for a traditional IRA) or by code J, T or Q in box 7 (for a Roth IRA).  TurboTax does not enforce the limit on the number of distributions eligible to be rolled over, so it's possible in TurboTax to report amounts as rolled over when they were, in fact, not permitted to be rolled over.  Distributions from a qualified retirement plan like a 401(k) and distributions from a traditional IRA being converted to a Roth IRA are not subject to this rollover limitation.

There is no box 4b on the 1099R there is a G in Box 7.

No.  The line 4b is on your actual 1040 tax return.   4b is the taxable amount of a IRA Distribution, rollover or conversion.

The Box 4b referred to is on the 1040 and for 2019 shows the taxable amount of IRA withdrawals. 

For 2019 we also have Box 4d for the taxable amount of pension and annuity withdrawals